Question 12 Marks
$2-\sqrt{5},2+\sqrt{5}$
Answer$\text { Let } \alpha=2-\sqrt{5} \text { and } \beta=2+\sqrt{5}$
$\therefore \alpha+\beta=2-\sqrt{5}+2+\sqrt{5}=4 \text { and } \alpha \beta=(2-\sqrt{5})(2+\sqrt{5})=4-5=1$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\therefore x^2-(4) x+(1)=0 $
$\therefore x^2-4 x+1=0$
View full question & answer→Question 22 Marks
$\frac{1}{2},-\frac{1}{2}$
AnswerLet $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$
$\therefore \alpha+\beta=\frac{1}{2}-\frac{1}{2}=0 \text { and } \alpha \beta=\frac{1}{2} \times-\frac{1}{2}=-\frac{1}{4}$
$\therefore$ and quadratic equation is, $x ^2-(\alpha+\beta) x +\alpha \beta=0$
$\therefore x ^2-(0) x +\left(-\frac{1}{4}\right)=0$
$\therefore x ^2-\frac{1}{4}=0 $
$\therefore 4 x ^2-1=0$
View full question & answer→Question 32 Marks
AnswerLet $\alpha=3$ and $\beta=-10$
$\therefore \alpha+\beta=3-10=-7 \text { and } \alpha \beta=3 \times-10=-30$
$\therefore$ and quadratic equation is, $x ^2-(\alpha+\beta) x +\alpha \beta=0$
$\therefore x ^2-(-7) x +(-30)=0$
$\therefore x ^2+7 x -30=0$
View full question & answer→Question 42 Marks
AnswerLet $\alpha=0$ and $\beta=4$
$\therefore \alpha+\beta=0+4=4 \text { and } \alpha \beta=0 \times 4=0$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\therefore x ^2-(4) x +(0)=0 $
$\therefore x ^2-4 x =0$
View full question & answer→Question 52 Marks
Determine the nature of roots of the following quadratic equation.
$m^2+2 m+9=0$
Answer$m ^2+2 m+9=0$ compare with $ax ^2+ bx + c =0$
$\Rightarrow a =1, b=2$ and $c =9$
$\therefore b ^2-4 ac =2^2-4(1)(9)$
$=4-36$
$=-32$
$\therefore b ^2-4 ac <0$.hence, roots are not real.
View full question & answer→Question 62 Marks
Determine the nature of roots of the following quadratic equation.
$2 y^2-7 y+2=0$
Answer$2 y ^2-7 y +2=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =2, b=-7 \text { and } c =2 $
$ \therefore b ^2-4 ac =-7^2-4(2)(2) $
$=49-16 $
$ =23$
$ \therefore b ^2-4 ac >0 . \text { Hence, roots are real and unequal }$
View full question & answer→Question 72 Marks
Determine the nature of roots of the following quadratic equation.
$x^2-4 x+4=0$
Answer$x ^2-4 x +4=0 \text { compare with } ax ^2+ bx + c =0$
$ \Rightarrow a =1, b=-4 \text { and } c =4 $
$\therefore b ^2-4 ac =-4^2-4(1)(4) $
$ =16-16 $
$ =0 $
$ \therefore b ^2-4 ac =0 \text {.hence,roots are real and equal }$
View full question & answer→Question 82 Marks
Find the value of discriminant.
$\sqrt{2} x ^2+4 x +2 \sqrt{2}=0$
Answer$\sqrt{2} x ^2+4 x +2 \sqrt{2}=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =\sqrt{2}, b=4 \text { and } c =2 \sqrt{2} $
$\therefore b ^2-4 ac =4^2-4(\sqrt{2})(2 \sqrt{2}) $
$ =16-16 $
$ =0$
View full question & answer→Question 92 Marks
Find the value of discriminant.
$2y^2 – 5y + 10 = 0$
View full question & answer→Question 102 Marks
Find the value of discriminant.
$x^2+7 x-1=0$
Answer$x^2+7 x-1=0 \text { compare with } ax^2+b x+c=0$
$ \Rightarrow a=1, b=7 \text { and } c=-1 $
$\therefore b^2-4 a c=7^2-4(1)(-1) $
$ =49+4$
$ =53$
View full question & answer→Question 112 Marks
Solve the following quadratic equation by factorization.
2m (m-24) = 50
Answer$2 m(m-24)=50 $
$2 m^2-48 m-50=0$
$\Rightarrow 2 m^2-50 m+2 m-50=0 $
$\Rightarrow 2 m(m-25)+2(m-25)=0 $
$\Rightarrow(2 m+2)(m-25)=0$
$\Rightarrow 2 m+2=0 \text { or } m-25=0 $
$\Rightarrow m=-1 \text { or } m=25$
Hence, $m =-1$ or $m =25$ are roots of the equation.
View full question & answer→Question 122 Marks
Solve the following quadratic equation by factorization.
$3 x^2-2 \sqrt{6} x+2=0$
Answer$3 x^2-\sqrt{6} x-\sqrt{6} x+2=0 $
$ \Rightarrow \sqrt{3} x(\sqrt{3} x-\sqrt{2})-\sqrt{2}(\sqrt{3} x-\sqrt{2})=0$
$ \Rightarrow(\sqrt{3} x-\sqrt{2})(\sqrt{3} x-\sqrt{2})=0$
$\Rightarrow(\sqrt{3} x-\sqrt{2})=0 \text { or }(\sqrt{3} x-\sqrt{2})=0$
$ x=\frac{\sqrt{2}}{\sqrt{3}} \text { or } x=\frac{\sqrt{2}}{\sqrt{3}}$
View full question & answer→Question 132 Marks
Solve the following quadratic equation by factorization.
$\sqrt{2 x^2}+7 x+5 \sqrt{2}=0 $ to solve this quadratic equation by factorization, complete the following activity.
Answer$\sqrt{2 x^2}+7 x+5 \sqrt{2}=0 $
$\sqrt{2} x^2+5 x+2 x+5 \sqrt{2}=0 $
$x(\sqrt{2} x+5)+\sqrt{2}(\sqrt{2} x+5)=0 $
$(x+\sqrt{2})(\sqrt{2} x+5)=0 $
$(x+\sqrt{2})=0 \text { or }(\sqrt{2} x+5)=0 $
$x=-\frac{5}{\sqrt{2}} \text { or } x=-\sqrt{2}$
$\therefore-\frac{5}{\sqrt{2}}$ and $-\sqrt{2}$ are roots of the equation.
View full question & answer→Question 142 Marks
Solve the following quadratic equation by factorization.
$6x - \frac{2}{x} = 1$
Answer$6 x^2-2=x $
$\Rightarrow 6 x^2-x-2=0 $
$\Rightarrow 6 x^2+3 x-4 x-2=0 $
$\Rightarrow 3 x(2 x+1)-2(2 x+1)=0 $
$\Rightarrow(3 x-2)(2 x+1)=0 $
$3 x-2=0 \Rightarrow 3 x=2 \Rightarrow x=\frac{2}{3} $
$2 x+1=0 \Rightarrow 2 x=-1 \Rightarrow x=-\frac{1}{2}$
Hence, $x =\frac{2}{3}$ and $x =-\frac{1}{2}$ are roots of the equation.
View full question & answer→Question 152 Marks
Solve the following quadratic equation by factorization.
$2 x ^2-2 x +\frac{1}{2}=0 $
Answer$2 x ^2-2 x +\frac{1}{2}=0 $
$\Rightarrow 4 x ^2-4 x +1=0 $
$\Rightarrow 4 x ^2-2 x -2 x +1 $
$\Rightarrow 2 x(2 x-1)-1(2 x-1) $
$\Rightarrow(2 x-1)(2 x-1) $
$\Rightarrow 2 x-1=0 \Rightarrow x=\frac{1}{2}, \frac{1}{2}$
Hence $x=\frac{1}{2}, \frac{1}{2}$ are roots of the equation
View full question & answer→Question 162 Marks
Solve the following quadratic equation by factorization.
$5 m^2=22 m+15$
Answer$5 m^2-22 m-15=0 $
$\Rightarrow 5 m^2-3 m+25 m-15 $
$\Rightarrow m (5 m-3)+5(5 m-3) $
$\Rightarrow( m +5)(5 m-3) $
$m +5=0 \Rightarrow m =-5$
$5 m-3=0 \Rightarrow 5 m=3 \Rightarrow m =\frac{3}{5}$
$\therefore$ Hence, $m =-5$ and $m =\frac{3}{5}$ are roots of the equation.
View full question & answer→Question 172 Marks
Solve the following quadratic equation by factorization.
$2y^2 + 27y + 13 = 0$
Answer$2 y^2+27 y+13=0 $
$\Rightarrow 2 y^2+26 y+y+13=0 $
$\Rightarrow 2 y(y+13)+(y+13)=0 $
$\Rightarrow(2 y+1)(y+13)=0 $
$2 y+1=0 \Rightarrow 2 y=-1 \Rightarrow y=-\frac{1}{2} $
$y+13=0 \Rightarrow y=-13$
Hence, $y =-13$ and $y =-\frac{1}{2}$ are roots of the equation.
View full question & answer→Question 182 Marks
Solve the following quadratic equation by factorization.
$x^2+x-20=0$
Answer$x^2+x-20=0 $
$\Rightarrow x^2+5 x-4 x-20=0$
$\Rightarrow x(x+5)-4(x+5)=0$
$\Rightarrow(x+5)(x-4)=0 $
$x+5=0 \Rightarrow x=-5$
$x-4=0 \Rightarrow x=4$
Hence, $x =-5$ and $x =4$ are roots of the equation.
View full question & answer→Question 192 Marks
Solve the following quadratic equation by factorization.
$m^2-11=0$
Answer$m ^2-11=0 $
$\Rightarrow m ^2=11 $
$\Rightarrow m =\sqrt{11}$
$\Rightarrow m = \pm 11$
Hence,$m= \pm 11$ are roots of the equation.
View full question & answer→Question 202 Marks
Solve the following quadratic equation by factorization.
$7 m^2=21 m$
Answer$7 m^2-21 m=0$
$\Rightarrow 7 m( m -3)=0 $
$\Rightarrow 7 m=0 \text { or } m -3=0 $
$\Rightarrow m =0 \text { or } m =3$
Hence, $m =0$ or $m =3$ are roots of the equation.
View full question & answer→Question 212 Marks
Solve the following quadratic equation by factorization.
$25 m^2=9$
Answer$25 m^2=9 $
$\Rightarrow m ^2=\frac{9}{25}$
$\Rightarrow m =\sqrt{\frac{9}{25}} $
$\Rightarrow m = \pm \frac{3}{5}$
Hence, $m= \pm \frac{3}{5}$ are roots of the equation.
View full question & answer→Question 222 Marks
Solve the following quadratic equation by factorization.
$x^2-15 x+54=0$
Answer
$x^2-15 x+54=0 $
$\Rightarrow x^2-6 x-9 x+54=0$
$\Rightarrow x(x-6)-9(x-6)=0 $
$\Rightarrow(x-6)(x-9)=0 $
$x-6=0 \Rightarrow x=6 $
$x-9=0 \Rightarrow x=9$
Hence, $x =6$ and $x =9$ are roots of the equation.
View full question & answer→Question 232 Marks
Determine the nature of roots for each of the quadratic equation.
$m^2-2 m+1=0$
Answer$m ^2-2 m+1=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =1, b=-2 \text { and } c =1 $.
$ \therefore b ^2-4 ac =-2^2-4(1)(1) $
$ =4-4 $
$ =0 $
$ \therefore b ^2-4 ac =0 $.hence,roots are real and equal.
View full question & answer→Question 242 Marks
Determine the nature of roots for each of the quadratic equation.
$\sqrt{3} x^2+\sqrt{2} x-2 \sqrt{3}=0$
Answer$\sqrt{3} x^2+\sqrt{2} x+2 \sqrt{3}=0 \text { compare with } a x^2+b x+c=0 $
$\Rightarrow a=\sqrt{3}, b=\sqrt{2} \text { and } c=-2 \sqrt{3} $
$\therefore b^2-4 a c=\sqrt{2}^2-4(\sqrt{3})(-2 \sqrt{3}) $
$=2+24 $
$=26$
$\therefore b ^2-4 ac >0$.hence, roots are real and umequal.
View full question & answer→Question 252 Marks
Determine the nature of roots for each of the quadratic equation.
$3 x^2-5 x+7=0$
Answer$3 x^2-5 x+7=0$ compare with $a x^2+b x+c=0$
$\Rightarrow a =3, b=-5$ and $c =7$
$\therefore b ^2-4 ac =-5^2-4(3)(7)$
$=25-147$
$=-122$
$\therefore b ^2-4 ac <0$.hence, roots are not real.
View full question & answer→Question 262 Marks
Find k if $x =3$ is a root of equation $k x^2-10 x +3=0$.
Answer$ kx ^2-10 x +3=0 \text { Put } x =3 $
$ \Rightarrow k (3)^2-10 \times 3+3=0 $
$ \Rightarrow 9 k -30+3=0$
$\Rightarrow 9 k =30-3 $
$ \Rightarrow 9 k =27 $
$ \Rightarrow k =\frac{27}{9}=3$
View full question & answer→Question 272 Marks
One of the roots of quadratic equation $2 x^2+k x-2=0$ is -2 , find $k$.
Answer$2 x ^2+ kx -2=0 $
$ \Rightarrow 2 \times-2^2-2 k -2=0$
$ \Rightarrow 8-2-2 k =0$
$\Rightarrow 6=2 k$
$ k =3$
View full question & answer→Question 282 Marks
Find the value of discriminant for each of the following equation.
$\sqrt{5} x^2-x-\sqrt{5}=0$
Answer$\sqrt{5} x^2-x-\sqrt{5}=0 \text { compare with } a x^2+b x+c=0 $
$ \Rightarrow a=\sqrt{5}, b=-1 \text { and } c=-\sqrt{5} $
$ \therefore b^2-4 a c=-1^2-4(\sqrt{5})(-\sqrt{5}) $
$ =1+20 $
$ =21$
View full question & answer→Question 292 Marks
Find the value of discriminant for each of the following equation.
$5 m^2-m=0$
Answer$5 m^2- m =0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =5, b=-1 \text { and } c =0 $
$ \therefore b ^2-4 ac =-1^2-4(5)(0) $
$ =1$
View full question & answer→Question 302 Marks
Find the value of discriminant for each of the following equation.
$2 y^2-y+2=0$
Answer$2 y^2-y+2=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =2, b=-1 \text { and } c =2 $
$ \therefore b ^2-4 ac =-1^2-4(2)(2) $
$ =1-16 $
$=-15
View full question & answer→Question 312 Marks
Obtain the quadratic equation if roots are $-3,-7$.
AnswerLet $\alpha=-3$ and $\beta=-7$
$ \therefore \alpha+\beta=(-3)+(-7)=-10 \text { and } \alpha \times \beta=(-3) \times(-7)=21$
$\therefore \text { and quadratic equation is, } x^2-(\alpha+\beta) x+\alpha \beta=0$
$\therefore x^2-(-10) x+21=0$
$\therefore x^2+10 x+21=0 $
View full question & answer→Question 322 Marks
Determine nature of roots of the quadratic equations : √3x² + 2√3x + 3 = 0
Question 332 Marks
Determine nature of roots of the quadratic equations : x² + 2x - 9 = 0
Question 342 Marks
Determine nature of roots of the quadratic equations : 2x² - 5x + 7 = 0
Question 352 Marks
View full question & answer→Question 362 Marks
View full question & answer→Question 372 Marks
$2 x^2-7 x+6=0$ check whether$x=-2$ are solutions of the equations.
AnswerLet $x=-2$ in $2 x^2-7 x+6$
\*
\begin{aligned}
2 x^2-7 x+6= & 2(-2)^2-7(-2)+6 \\
& =2 \times 4+14+6 \\
& =28 \neq 0
\end{aligned}
$
$\therefore x=-2$ is not a solution of the equation.
View full question & answer→Question 382 Marks
$2 x^2-7 x+6=0$ check whether (i) $x=\frac{3}{2}$,
AnswerPut $x=\frac{3}{2}$ in the polynomial $2 x^2-7 x+6$
$2 x^2-7 x+6=2\left(\frac{3}{2}\right)^2-7\left(\frac{3}{2}\right)+6$
$32$
$=2 \times \frac{9}{4}-\frac{21}{2}+6$
$=\frac{9}{2}-\frac{21}{2}+\frac{12}{2}=0 $
$\therefore x=\frac{3}{2}$ is a solution of the equation.
View full question & answer→Question 392 Marks
Solve the following quadratic equation by using formula method:
$9 y^2-5 y-4=0$
Answer1 and $\frac{-4}{9}$
View full question & answer→Question 402 Marks
Solve the following quadratic equation by using formula method:
$4 x^2+x-5=0$
Answer1 and $\frac{-5}{4}$
View full question & answer→Question 412 Marks
Solve the following quadratic equation by using formula method:
$x^2+4 x-1=0$
Answer$-2+\sqrt{5}$ and $-2-\sqrt{5}$
View full question & answer→Question 422 Marks
Solve the following quadratic equation by using formula method:
$5 m^2+5 m=1$
Answer$\frac{-5+3 \sqrt{5}}{10}$ and $\frac{-5-3 \sqrt{5}}{10}$
View full question & answer→Question 432 Marks
Solve the following quadratic equation by using formula method:
$3 x^2+8 x+3=0$
Answer$\frac{-4+\sqrt{7}}{3}$ and $\frac{-4-\sqrt{7}}{3}$
View full question & answer→Question 442 Marks
Solve the following quadratic equation by using formula method:
$x^2+2 x-7=0$
Answer$-1+2 \sqrt{2}$ and $-1-2 \sqrt{2}$
View full question & answer→Question 452 Marks
Solve the following quadratic equation by factorization method:
$m^2-7=0$
Answer$x=\sqrt{7}$ or $x=-\sqrt{7}$
View full question & answer→Question 462 Marks
Solve the following quadratic equation by factorization method:
$7 x^2+4 x-20=0$
Answer$x=-2$ or $x=\frac{10}{7}$
View full question & answer→Question 472 Marks
Solve the following quadratic equation by factorization method:
$x^2-3 \sqrt{3} x+6=0$
Answer$x=\sqrt{3}$ or $x=2 \sqrt{3}$
View full question & answer→Question 482 Marks
Solve the following quadratic equation by factorization method:
$16 x^2-24 x=0$
Answer$x=0$ or $x=\frac{3}{2}$
View full question & answer→Question 492 Marks
Solve the following quadratic equation by factorization method:
$x^2-13 x+30=0$
View full question & answer→Question 502 Marks
Solve the following quadratic equation by factorization method:
$64 m^2-625=0$
Answer$m=\frac{-25}{8}$ or $m=\frac{25}{8}$
View full question & answer→Question 512 Marks
Solve the following quadratic equation by factorization method:
$3 y^2-14 y+8=0$
Answer$y=4$ or $y=\frac{2}{3}$
View full question & answer→Question 522 Marks
Solve the following quadratic equation by factorization method:
$x^2-5 x-36=0$
View full question & answer→Question 532 Marks
Solve the following quadratic equation by completing square method:
$6 m^2+m=2$
Answer$m=\frac{1}{2}$ or $m=\frac{-2}{3}$
View full question & answer→Question 542 Marks
Solve the following quadratic equation by completing square method:
$4 p^2+7=12 p$
Answer$p=\frac{3+\sqrt{2}}{2}$ or $p=\frac{3-\sqrt{2}}{2}$
View full question & answer→Question 552 Marks
Solve the following quadratic equation by completing square method:
$3 y^2+7 y+1=0$
Answer$y=\frac{-7+\sqrt{37}}{6}$ or $m=\frac{-7-\sqrt{37}}{6}$
View full question & answer→Question 562 Marks
Solve the following quadratic equation by completing square method:
$x^2+3 x+1=0$
Answer$m=\frac{-3+\sqrt{5}}{2}$ or $m=\frac{-3-\sqrt{5}}{2}$
View full question & answer→Question 572 Marks
Solve the following quadratic equation by completing square method:
$m^2-2 m-1=0$
Answer$m=1+\sqrt{2}$ or $m=1-\sqrt{2}$
View full question & answer→Question 582 Marks
Solve the following quadratic equation by completing square method:
$x^2+8 x+15=0$
View full question & answer→Question 592 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$4 x^2-8 x+9=0$
View full question & answer→Question 602 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$2 x^2-3 x-4=0$
View full question & answer→Question 612 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$x^2-8 x+16=0$
View full question & answer→Question 622 Marks
Find the value of discriminant for of the following quadratic equation:
$3 x^2+2 x+1=0$
View full question & answer→Question 632 Marks
Find the value of discriminant for of the following quadratic equation:
$x^2+4 x+1=0$
View full question & answer→Question 642 Marks
Find the value of discriminant for of the following quadratic equation:
$x^2+4 x+4=0$
View full question & answer→Question 652 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$(x+5)(x-11)$
Answer$x^2-6 x-55=0$ and $a=1, b=-6, c=-55$
View full question & answer→Question 662 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$x-\frac{6}{x}=5$
Answer$x^2-5 x-6=0$ and $a=1, b=-5, c=-6$
View full question & answer→Question 672 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$\frac{x^2-7}{x}=7$
Answer$x^2-7 x-7=0$ and $a=1, b=-7, c=-7$
View full question & answer→Question 682 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$m(m-7)=0$
Answer$m^2-7 m+0=0$ and $a=1, b=-7, c=0$
View full question & answer→Question 692 Marks
Determine whether the given values of $x$ are the roots of given quadratic equation $6 x^2-x-2=0$,$x=\frac{-1}{2}, x=5$
Answer$x=\frac{-1}{2}$ is the root and $x=5$ is not the root of given equation.
View full question & answer→Question 702 Marks
If one root of the quadratic equation $3 y^2-k y+8=0$ is $\frac{2}{3}$, then find the value of $k$.
View full question & answer→Question 712 Marks
If $x=9$ is one root of the quadratic equation $x^2-11 x+k=0$, then find the value of $k$.
View full question & answer→Question 722 Marks
Determine the nature of roots for each of the quadratic equation.
m2 – 2m + 1 = 0
Answer
$\begin{array}{l} m ^2-2 m +1=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =1, b =-2 \text { and } c =1 \\ \therefore b ^2-4 ac =-2^2-4(1)(1) \\ =4-4 \\ =0 \\ \therefore b ^2-4 ac =0 \text {. hence,roots are real and equal. }\end{array}$
View full question & answer→Question 732 Marks
Determine the nature of roots for each of the quadratic equation.
$\sqrt{3} x^2+\sqrt{2} x-2 \sqrt{3}=0$
Answer
$\begin{array}{l}
\sqrt{3} x^2+\sqrt{2} x+2 \sqrt{3}=0 \text { compare with } a x^2+b x+c=0 \\
\Rightarrow a=\sqrt{3}, b=\sqrt{2} \text { and } c=-2 \sqrt{3} \\
\therefore b^2-4 a c=\sqrt{2}^2-4(\sqrt{3})(-2 \sqrt{3}) \\
=2+24 \\
=26
\end{array}$
$\therefore b ^2-4 ac >0$. hence, roots are real and umequal .
View full question & answer→Question 742 Marks
Determine the nature of roots for each of the quadratic equation.
3x2 – 5x + 7 = 0
Answer
$\begin{array}{l}3 x ^2-5 x +7=0 \text { compare with } a x^2+ bx + c =0 \\ \Rightarrow a =3, b =-5 \text { and } c =7 \\ \therefore b ^2-4 ac =-5^2-4(3)(7) \\ =25-147 \\ =-122 \\ \therefore b ^2-4 ac <0 \text {.hence, roots are not real. }\end{array}$
View full question & answer→Question 752 Marks
One of the roots of quadratic equation 2x2 + kx – 2 = 0 is -2, find k.
Answer
$\begin{array}{l}2 x ^2+ kx -2=0 \\ \Rightarrow 2 \times-2^2-2 k -2=0 \\ \Rightarrow 8-2-2 k =0 \\ \Rightarrow 6=2 k \\ k =3\end{array}$
View full question & answer→Question 762 Marks
Form the quadratic equation from the roots given below : $2-\sqrt{5}, 2+\sqrt{5}$
AnswerLet $\alpha=2-\sqrt{5}$ and $\beta=2+\sqrt{5}$
$\therefore \alpha+\beta=2-\sqrt{5}+2+\sqrt{5}=4 \text { and } \alpha \beta=(2-\sqrt{5})(2+\sqrt{5})=4-5=1$
$\therefore$ and quadratic equation is, $x ^2-(\alpha+\beta) x +\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(4) x +(1)=0 \\
\therefore x ^2-4 x +1=0
\end{array}$
View full question & answer→Question 772 Marks
Form the quadratic equation from the roots given below : $\frac{1}{2},-\frac{1}{2}$
AnswerLet $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$
$\therefore \alpha+\beta=\frac{1}{2}-\frac{1}{2}=0 \text { and } \alpha \beta=\frac{1}{2} \times-\frac{1}{2}=-\frac{1}{4}$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(0) x +\left(-\frac{1}{4}\right)=0 \\
\therefore x ^2-\frac{1}{4}=0 \\
\therefore 4 x ^2-1=0
\end{array}$
View full question & answer→Question 782 Marks
Form the quadratic equation from the roots given below : 3 and -10
AnswerLet $\alpha=3$ and $\beta=-10$
$\therefore \alpha+\beta=3-10=-7$ and $\alpha \beta=3 \times-10=-30$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(-7) x +(-30)=0 \\
\therefore x ^2+7 x -30=0
\end{array}$
View full question & answer→Question 792 Marks
Form the quadratic equation from the roots given below : 0 and 4
AnswerLet $\alpha=0$ and $\beta=4$
$\therefore \alpha+\beta=0+4=4$ and $\alpha \beta=0 \times 4=0$
$\therefore$ and quadratic equation is, $x ^2-(\alpha+\beta) x +\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(4) x +(0)=0 \\
\therefore x ^2-4 x =0
\end{array}$
View full question & answer→Question 802 Marks
Determine the nature of roots of the following quadratic equation.
m2 + 2m + 9 = 0
Answer
$\begin{array}{l} m ^2+2 m +9=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =1, b =2 \text { and } c =9 \\ \therefore b ^2-4 ac =2^2-4(1)(9) \\ =4-36 \\ =-32 \\ \therefore b ^2-4 ac <0 \text {. hence, roots are not real. }\end{array}$
View full question & answer→Question 812 Marks
Determine the nature of roots of the following quadratic equation.
2y2 – 7y + 2 = 0
Answer
$\begin{array}{l}2 y^2-7 y+2=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=2, b=-7 \text { and } c=2 \\ \therefore b^2-4 a c=-7^2-4(2)(2) \\ =49-16 \\ =23 \\ \therefore b^2-4 a c>0 \text {. Hence, roots are real and unequal }\end{array}$
View full question & answer→Question 822 Marks
Determine the nature of roots of the following quadratic equation.
x2 – 4x + 4 = 0
Answer
$\begin{array}{l} x ^2-4 x +4=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =1, b =-4 \text { and } c =4 \\ \therefore b ^2-4 ac =-4^2-4(1)(4) \\ =16-16 \\ =0 \\ \therefore b ^2-4 ac =0 \text {. hence, roots are real and equal }\end{array}$
View full question & answer→Question 832 Marks
Find the value of discriminant.
$\sqrt{2} x^2+4 x+2 \sqrt{2}=0$
Answer
$\begin{array}{l}\sqrt{2} x^2+4 x+2 \sqrt{2}=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=\sqrt{2}, b=4 \text { and } c=2 \sqrt{2} \\ \therefore b^2-4 a c=4^2-4(\sqrt{2})(2 \sqrt{2}) \\ =16-16 \\ =0\end{array}$
View full question & answer→Question 842 Marks
Find the value of discriminant.
2y2 – 5y + 10 = 0
Answer
$\begin{array}{l}2 y^2-5 y+10=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=2, b=-5 \text { and } c=10 \\ \therefore b^2-4 a c=-5^2-4(2)(10) \\ =25-80 \\ =-55\end{array}$
View full question & answer→Question 852 Marks
Find the value of discriminant.
x2 + 7x – 1 = 0
Answer
$\begin{array}{l} x ^2+7 x -1=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =1, b =7 \text { and } c =-1 \\ \therefore b ^2-4 ac =7^2-4(1)(-1) \\ =49+4 \\ =53\end{array}$
View full question & answer→Question 862 Marks
Solve the following quadratic equation by factorization.
m2 - 11 = 0
Answer
$\begin{array}{l}
m ^2-11=0 \\
\Rightarrow m ^2=11 \\
\Rightarrow m =\sqrt{11} \\
\Rightarrow m = \pm 11
\end{array}$
Hence, $m= \pm 11$ are roots of the equation
View full question & answer→Question 872 Marks
Solve the following quadratic equation by factorization.
7m2 = 21m
Answer
$\begin{array}{l}
7 m ^2-21 m =0 \\
\Rightarrow 7 m ( m -3)=0 \\
\Rightarrow 7 m =0 \text { or } m -3=0 \\
\Rightarrow m =0 \text { or } m =3
\end{array}$
Hence, $m =0$ or $m =3$ are roots of the equation.
View full question & answer→Question 882 Marks
Solve the following quadratic equation by factorization.
25m2 = 9
Answer
$\begin{array}{l}
25 m ^2=9 \\
\Rightarrow m ^2=\frac{9}{25} \\
\Rightarrow m =\sqrt{\frac{9}{25}} \\
\Rightarrow m = \pm \frac{3}{5} \\
\text { Hence, } m = \pm \frac{3}{5} \text { are roots of the equation. }
\end{array}$
Hence, $m = \pm \frac{3}{5}$ are roots of the equation.
View full question & answer→Question 892 Marks
Solve the following quadratic equation by factorization.
$3 x^2-2 \sqrt{6} x+2=0$
Answer
$\begin{array}{l}3 x^2-\sqrt{6} x-\sqrt{6} x+2=0 \\ \Rightarrow \sqrt{3} x(\sqrt{3} x-\sqrt{2})-\sqrt{2}(\sqrt{3} x-\sqrt{2})=0 \\ \Rightarrow(\sqrt{3} x-\sqrt{2})(\sqrt{3} x-\sqrt{2})=0 \\ \Rightarrow(\sqrt{3} x-\sqrt{2})=0 \text { or }(\sqrt{3} x-\sqrt{2})=0 \\ x=\frac{\sqrt{2}}{\sqrt{3}} \text { or } x=\frac{\sqrt{2}}{\sqrt{3}}\end{array}$
View full question & answer→Question 902 Marks
Solve the following quadratic equation by factorization. $\sqrt{2} x^2+7 x+5 \sqrt{2}=0$ to solve this quadratic equation by factorization, complete the following activity.
Answer
$\begin{array}{l}\sqrt{2 x^2}+7 x+5 \sqrt{2}=0 \\ \sqrt{2} x^2+5 x+2 x+5 \sqrt{2}=0 \\ x(\sqrt{2} x+5)+\sqrt{2}(\sqrt{2} x+5)=0 \\ (x+\sqrt{2})(\sqrt{2} x+5)=0 \\ (x+\sqrt{2})=0 \text { or }(\sqrt{2} x+5)=0 \\ x=-\frac{5}{\sqrt{2}} \text { or } x=-\sqrt{2} \\ \therefore-\frac{5}{\sqrt{2}} \text { and }-\sqrt{2} \text { are roots of the equation. }\end{array}$
View full question & answer→Question 912 Marks
Solve the following quadratic equation by factorization.
$6 x-\frac{2}{x}=1$
Answer
$\begin{array}{l}6 x^2-2=x \\ \Rightarrow 6 x^2-x-2=0 \\ \Rightarrow 6 x^2+3 x-4 x-2=0 \\ \Rightarrow 3 x(2 x+1)-2(2 x+1)=0 \\ \Rightarrow(3 x-2)(2 x+1)=0 \\ 3 x-2=0 \Rightarrow 3 x=2 \Rightarrow x=\frac{2}{3} \\ 2 x+1=0 \Rightarrow 2 x=-1 \Rightarrow x=-\frac{1}{2}\end{array}$
Hence, ${ }^x=\frac{2}{3}$ and $x=-\frac{1}{2}$ are roots of the equation.
View full question & answer→Question 922 Marks
Solve the following quadratic equation by factorization.
$2 x^2-2 x+\frac{1}{2}=0$
Answer
$\begin{array}{l}
2 x ^2-2 x +\frac{1}{2}=0 \\
\Rightarrow 4 x ^2-4 x +1=0 \\
\Rightarrow 4 x ^2-2 x -2 x +1 \\
\Rightarrow 2 x(2 x-1)-1(2 x-1) \\
\Rightarrow(2 x-1)(2 x-1) \\
\Rightarrow 2 x-1=0 \Rightarrow x=\frac{1}{2}, \frac{1}{2}
\end{array}$
Hence $x=\frac{1}{2}, \frac{1}{2}$ are roots of the equation
View full question & answer→Question 932 Marks
Solve the following quadratic equation by factorization.
2m (m-24) = 50
Answer
$\begin{array}{l}
2 m(m-24)=50 \\
2 m^2-48 m-50=0 \\
\Rightarrow 2 m^2-50 m+2 m-50=0 \\
\Rightarrow 2 m(m-25)+2(m-25)=0 \\
\Rightarrow(2 m+2)(m-25)=0 \\
\Rightarrow 2 m+2=0 \text { or } m-25=0 \\
\Rightarrow m=-1 \text { or } m=25
\end{array}$
Hence, $m =-1$ or $m =25$ are roots of the equation.
View full question & answer→Question 942 Marks
Solve the following quadratic equation by factorization.
5m2 = 22m + 15
Answer
$\begin{array}{l}5 m ^2-22 m -15=0 \\ \Rightarrow 5 m ^2-3 m +25 m -15 \\ \Rightarrow m (5 m -3)+5(5 m -3) \\ \Rightarrow( m +5)(5 m -3) \\ m +5=0 \Rightarrow m =-5 \\ 5 m -3=0 \Rightarrow 5 m =3 \Rightarrow m =\frac{3}{5} \\ \therefore \text { Hence, } m =-5 \text { and } m =\frac{3}{5} \text { are roots of the equation. }\end{array}$
View full question & answer→Question 952 Marks
Solve the following quadratic equation by factorization.
2y2 + 27y + 13 = 0
Answer
$\begin{array}{l}
2 y^2+27 y+13=0 \\
\Rightarrow 2 y^2+26 y+y+13=0 \\
\Rightarrow 2 y(y+13)+(y+13)=0 \\
\Rightarrow(2 y+1)(y+13)=0 \\
2 y+1=0 \Rightarrow 2 y=-1 \Rightarrow y=-\frac{1}{2} \\
y+13=0 \Rightarrow y=-13
\end{array}$
Hence, ${ }^y=-13$ and $y=-\frac{1}{2}$ are roots of the equation.
View full question & answer→Question 962 Marks
Solve the following quadratic equation by factorization.
x2 + x – 20 = 0
Answer
$\begin{array}{l}
x^2+x-20=0 \\
\Rightarrow x^2+5 x-4 x-20=0 \\
\Rightarrow x(x+5)-4(x+5)=0 \\
\Rightarrow(x+5)(x-4)=0 \\
x+5=0 \Rightarrow x=-5 \\
x-4=0 \Rightarrow x=4 z
\end{array}$
Hence, $x=-5$ and $x=4$ are roots of the equation.
View full question & answer→Question 972 Marks
Solve the following quadratic equation by factorization.
x2 – 15x + 54 = 0
Answer
$\begin{array}{l}
x^2-15 x+54=0 \\
\Rightarrow x^2-6 x-9 x+54=0 \\
\Rightarrow x(x-6)-9(x-6)=0 \\
\Rightarrow(x-6)(x-9)=0 \\
x-6=0 \Rightarrow x=6 \\
x-9=0 \Rightarrow x=9
\end{array}$
Hence, $x=6$ and $x=9$ are roots of the equation.
View full question & answer→Question 982 Marks
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Answer
$\begin{array}{l} kx ^2-10 x +3=0 \text { Put } x =3 \\ \Rightarrow k (3)^2-10 \times 3+3=0 \\ \Rightarrow 9 k -30+3=0 \\ \Rightarrow 9 k =30-3 \\ \Rightarrow 9 k =27 \\ \Rightarrow k =\frac{27}{9}=3\end{array}$
View full question & answer→Question 992 Marks
Find the value of discriminant for each of the following equation.
$\sqrt{5} x^2-x-\sqrt{5}=0$
Answer
$\begin{array}{l}\sqrt{5} x^2-x-\sqrt{5}=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=\sqrt{5}, b=-1 \text { and } c=-\sqrt{5} \\ \therefore b^2-4 a c=-1^2-4(\sqrt{5})(-\sqrt{5}) \\ =1+20 \\ =21\end{array}$
View full question & answer→Question 1002 Marks
Find the value of discriminant for each of the following equation.
5m2 – m = 0
Answer
$\begin{array}{l}5 m^2-m=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=5, b=-1 \text { and } c=0 \\ \therefore b^2-4 a c=-1^2-4(5)(0) \\ =1\end{array}$
View full question & answer→Question 1012 Marks
Find the value of discriminant for each of the following equation.
2y2 – y + 2 = 0
Answer
$\begin{array}{l}2 y ^2- y +2=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =2, b =-1 \text { and } c =2 \\ \therefore b ^2-4 ac =-1^2-4(2)(2) \\ =1-16 \\ =-15\end{array}$
View full question & answer→Question 1022 Marks
Obtain the quadratic equation if roots are $-3,-7$.
AnswerLet $\alpha=-3$ and $\beta=-7$
$
\begin{array}{l}
\therefore \alpha+\beta=(-3)+(-7)=-10 \text { and } \alpha \times \beta=(-3) \times(-7)=21 \\
\therefore \text { and quadratic equation is, } x^2-(\alpha+\beta) x+\alpha \beta=0 \\
\therefore x^2-(-10) x+21=0 \\
\therefore x^2+10 x+21=0
\end{array}
$
View full question & answer→Question 1032 Marks
Determine nature of roots of the quadratic equations : x² + 2x - 9 = 0
Answer
$\begin{array}{l}
\text { Compare } x^2+2 x-9=0 \text { with } a x^2+b x+c=0 \\
a=1, b=2, c=-9 \\
\therefore b^2-4 a c=(2)^2-4 \times 1 \times-9 \\
\Delta=4+36=40 \\
\therefore b^2-4 a c>0
\end{array}$
$\therefore$ The roots of the equation are real and unequal.
View full question & answer→Question 1042 Marks
Determine nature of roots of the quadratic equations : √3x² + 2√3x + 3 = 0
AnswerCompare $\sqrt{3} x^2+2 \sqrt{3} x+\sqrt{3}=0$ with $a x^2+b x+c=0$
We get $a=\sqrt{3}, b=2 \sqrt{3}, c=\sqrt{3}$,
$\begin{aligned}
\therefore b^2-4 a c= & (2 \sqrt{3})^2-4 \times \sqrt{3} \times \sqrt{3} \\
& =4 \times 3-4 \times 3 \\
& =12-12 \\
& =0
\end{aligned}$
$\therefore b^2-4 a c=0$
$\therefore$ Roots of the equation are real and equal.
View full question & answer→Question 1052 Marks
Determine nature of roots of the quadratic equations : 2x² - 5x + 7 = 0
AnswerCompare $2 x^2-5 x+7=0$ with
$\begin{array}{c}
a x^2+b x+c=0 \\
a=2, b=-5, c=7, \\
\therefore b^2-4 a c=(-5)^2-4 \times 2 \times 7 \\
D =25-56 \\
D =-31 \\
\therefore b^2-4 a c<0
\end{array}$
$\therefore$ the roots of the equation are not real.
View full question & answer→Question 1062 Marks
Solve quadratic equation using formula : x² - 2x - 3 = 0
Answer
$\begin{array}{l}\text { comparing with } a x^2+b x+c=0 \\ \text { we get } a=1, b=-2, c=-3 \text {, } \\ \therefore b^2-4 a c=(-2)^2-4 \times 1 \times(-3)=4+12=16 \\ \therefore x=\frac{-(-2)+\sqrt{16}}{2} \text { or } x=\frac{-(-2)-\sqrt{16}}{2} \\ =\frac{2+4}{2} \text { or } \frac{2-4}{2} \\ =3 \text { or }-1\end{array}$
View full question & answer→Question 1072 Marks
AnswerMethod I : Completing the square.
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+8 x+16-16-48=0 \\
\therefore(x+4)^2-64=0 \\
\therefore(x+4)^2=64 \\
\therefore x+4=8 \text { or } x+4=-8 \\
\therefore x=4 \text { or } x=-12
\end{array}$
Method II : Factorisation
$\begin{array}{l}
x^2+8 x-48=0 \\
\therefore x^2+12 x-4 x-48=0 \\
\therefore x(x+12)-4(x+12)=0 \\
\therefore(x+12)(x-4)=0 \\
\therefore x+12=0 \text { or } x-4=0 \\
\therefore x=-12 \text { or } x=4
\end{array}$
View full question & answer→Question 1082 Marks
$2 x^2-7 x+6=0$ check whether (i) $x=\frac{3}{2}$, (ii)x=-2 are solutions of the equations.
AnswerPut $x=\frac{3}{2}$ in the polynomial $2 x^2-7 x+6$
$2 x^2-7 x+6=2\left(\frac{3}{2}\right)^2-7\left(\frac{3}{2}\right)+6$
$
\begin{array}{l}
=2 \times \frac{9}{4}-\frac{21}{2}+6 \\
=\frac{9}{2}-\frac{21}{2}+\frac{12}{2}=0
\end{array}
$
2.$\therefore x=\frac{3}{2}$ is a solution of the equation.
Let $x=-2$ in $2 x^2-7 x+6$
\begin{aligned}
2 x^2-7 x+6= & 2(-2)^2-7(-2)+6 \\
& =2 \times 4+14+6 \\
& =28\neq 0\end{aligned}
$\therefore x=-2$ is not a solution of the equation.
View full question & answer→Question 1092 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$x-\frac{6}{x}=5$
Answer$x^2-5 x-6=0$ and $a=1, b=-5, c=-6$
View full question & answer→Question 1102 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$(x+5)(x-11)$
Answer$x^2-6 x-55=0$ and $a=1, b=-6, c=-55$
View full question & answer→Question 1112 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$m(m-7)=0$
Answer$m^2-7 m+0=0$ and $a=1, b=-7, c=0$
View full question & answer→Question 1122 Marks
Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$\frac{x^2-7}{x}=7$
Answer$x^2-7 x-7=0$ and $a=1, b=-7, c=-7$
View full question & answer→Question 1132 Marks
Solve the following quadratic equation by using formula method:
$x^2+4 x-1=0$
Answer$-2+\sqrt{5}$ and $-2-\sqrt{5}$
View full question & answer→Question 1142 Marks
Solve the following quadratic equation by using formula method:
$x^2+2 x-7=0$
Answer$-1+2 \sqrt{2}$ and $-1-2 \sqrt{2}$
View full question & answer→Question 1152 Marks
Solve the following quadratic equation by using formula method:
$9 y^2-5 y-4=0$
Answer1 and $\frac{-4}{9}$
View full question & answer→Question 1162 Marks
Solve the following quadratic equation by using formula method:
$5 m^2+5 m=1$
Answer$\frac{-5+3 \sqrt{5}}{10}$ and $\frac{-5-3 \sqrt{5}}{10}$
View full question & answer→Question 1172 Marks
Solve the following quadratic equation by using formula method:
$4 x^2+x-5=0$
Answer1 and $\frac{-5}{4}$
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Solve the following quadratic equation by using formula method:
$3 x^2+8 x+3=0$
Answer$\frac{-4+\sqrt{7}}{3}$ and $\frac{-4-\sqrt{7}}{3}$
View full question & answer→Question 1192 Marks
Solve the following quadratic equation by factorization method:
$x^2-5 x-36=0$
View full question & answer→Question 1202 Marks
Solve the following quadratic equation by factorization method:
$x^2-3 \sqrt{3} x+6=0$
Answer$x=\sqrt{3}$ or $x=2 \sqrt{3}$
View full question & answer→Question 1212 Marks
Solve the following quadratic equation by factorization method:
$x^2-13 x+30=0$
View full question & answer→Question 1222 Marks
Solve the following quadratic equation by factorization method:
$m^2-7=0$
Answer$x=\sqrt{7}$ or $x=-\sqrt{7}$
View full question & answer→Question 1232 Marks
Solve the following quadratic equation by factorization method:
$7 x^2+4 x-20=0$
Answer$x=-2$ or $x=\frac{10}{7}$
View full question & answer→Question 1242 Marks
Solve the following quadratic equation by factorization method:
$64 m^2-625=0$
Answer$m=\frac{-25}{8}$ or $m=\frac{25}{8}$
View full question & answer→Question 1252 Marks
Solve the following quadratic equation by factorization method:
$3 y^2-14 y+8=0$
Answer$y=4$ or $y=\frac{2}{3}$
View full question & answer→Question 1262 Marks
Solve the following quadratic equation by factorization method:
$16 x^2-24 x=0$
Answer$x=0$ or $x=\frac{3}{2}$
View full question & answer→Question 1272 Marks
Solve the following quadratic equation by completing square method:
$x^2+8 x+15=0$
View full question & answer→Question 1282 Marks
Solve the following quadratic equation by completing square method:
$x^2+3 x+1=0$
Answer$m=\frac{-3+\sqrt{5}}{2}$ or $m=\frac{-3-\sqrt{5}}{2}$
View full question & answer→Question 1292 Marks
Solve the following quadratic equation by completing square method:
$m^2-2 m-1=0$
Answer$m=1+\sqrt{2}$ or $m=1-\sqrt{2}$
View full question & answer→Question 1302 Marks
Solve the following quadratic equation by completing square method:
$6 m^2+m=2$
Answer$m=\frac{1}{2}$ or $m=\frac{-2}{3}$
View full question & answer→Question 1312 Marks
Solve the following quadratic equation by completing square method:
$4 p^2+7=12 p$
Answer$p=\frac{3+\sqrt{2}}{2}$ or $p=\frac{3-\sqrt{2}}{2}$
View full question & answer→Question 1322 Marks
Solve the following quadratic equation by completing square method:
$3 y^2+7 y+1=0$
Answer$y=\frac{-7+\sqrt{37}}{6}$ or $m=\frac{-7-\sqrt{37}}{6}$
View full question & answer→Question 1332 Marks
If $x=9$ is one root of the quadratic equation $x^2-11 x+k=0$, then find the value of $k$.
View full question & answer→Question 1342 Marks
If one root of the quadratic equation $3 y^2-k y+8=0$ is $\frac{2}{3}$, then find the value of $k$.
View full question & answer→Question 1352 Marks
Find the value of discriminant for of the following quadratic equation:
$x^2+4 x+4=0$
View full question & answer→Question 1362 Marks
Find the value of discriminant for of the following quadratic equation:
$x^2+4 x+1=0$
View full question & answer→Question 1372 Marks
Find the value of discriminant for of the following quadratic equation:
$3 x^2+2 x+1=0$
View full question & answer→Question 1382 Marks
Determine whether the given values of $x$ are the roots of given quadratic equation $6 x^2-x-2=0$,$x=\frac{-1}{2}, x=5$
Answer$x=\frac{-1}{2}$ is the root and $x=5$ is not the root of given equation.
View full question & answer→Question 1392 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$x^2-8 x+16=0$
View full question & answer→Question 1402 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$4 x^2-8 x+9=0$
View full question & answer→Question 1412 Marks
Determine the nature of roots of the following quadratic equation from their discriminant:
$2 x^2-3 x-4=0$
View full question & answer→