MCQ 11 Mark
Choose the correct answer for the following question.
One of the roots of equation $x^2+m x-5=0$ is $2$; find m.
- A
$-2$
- B
$-\frac{1}{2}$
- ✓
$\frac{1}{2}$
- D
$2$
AnswerCorrect option: C. $\frac{1}{2}$
$x^2+m x-5=0$, Put value of $x=2$
$2^2+2 m=5 \Rightarrow 2 m=5-4 \Rightarrow m=\frac{1}{2}$
View full question & answer→MCQ 21 Mark
Choose the correct answer for the following question.
$\sqrt{5} m^2-\sqrt{5} m+\sqrt{5}=0$ which of the following statement is true for this given equation?
Answer$\sqrt{5} m^2+\sqrt{5} m+\sqrt{5}=0 \text { compare with } ax ^2+ bx + c =0 $
$\Rightarrow a =\sqrt{5}, b=\sqrt{5} \text { and } c =\sqrt{5}$
$ \therefore b ^2-4 ac =\sqrt{5}^2-4(\sqrt{5})(\sqrt{5}) $
$ =5-20$
$ =-15$
$ \therefore b ^2-4 ac <0 \text {.hence, roots are not real. }$
View full question & answer→Question 31 Mark
Choose the correct answer for the following question.
Out of the following equations, find the equation having the sum of its roots -5.
A. $3 x^2-15 x+3=0$
B. $x^2-5 x+3=0$
C. $x^2+3 x-5=0$
D. $3 x^2+15 x+3=0$
AnswerSum of the roots i.e. $\alpha+\beta=-\frac{b}{a}$
$\therefore$ in option $A, \alpha+\beta=-\frac{-15}{3}=5$
$\therefore$ in option $B, \alpha+\beta=-\frac{-5}{1}=5$
$\therefore$ in option $A, \alpha+\beta=-\frac{3}{1}=3$
$\therefore$ in option $A, \alpha+\beta=-\frac{15}{3}=-5$
View full question & answer→Question 41 Mark
Choose the correct answer for the following question.
Which of the following quadratic equations has roots 3, 5?
A. $x^2-15 x+8=0$
B. $x^2-8 x+15=0$
C. $x^2+3 x+5=0$
D. $x^2+8 x-15=0$
AnswerIn option A,
$\Rightarrow x^2-15 x+8=0$
$\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}=\frac{15 \pm \sqrt{-15^2-4(1)(8)}}{2 \times 1}=\frac{15 \pm \sqrt{225-80}}{2}=\frac{15 \pm \sqrt{145}}{2}$
In option B
$x^2-8 x+15=0$
$\Rightarrow x^2-5 x-3 x+15=0$
$\Rightarrow x(x-5)-3(x-5)=0$
$\Rightarrow(x-5)(x-3)=0$
$\Rightarrow x-5=0 \text { or } x-3=0$
$x=5 \text { and } x=3$
In option c,
$\Rightarrow x^2+3 x+5=0$
$\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}=\frac{-3 \pm \sqrt{3^2-4(1)(5)}}{2 \times 1}=\frac{-3 \pm \sqrt{9-20}}{2}=\frac{(-3 \pm \sqrt{-11})}{2}$
In option d
$x^2+8 x -15=0$
$\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}=\frac{-8 \pm \sqrt{8^2-4(1)(15)}}{2 \times 1}=\frac{-8 \pm \sqrt{64-60}}{2}=\frac{(-8 \pm 2)}{2}$
$x=\frac{-8+2}{2}=-\frac{6}{2}=-3 \text { or } x=\frac{-8-2}{2}=-\frac{10}{2}=-5$
View full question & answer→MCQ 51 Mark
Choose the correct answer for the following question.
For $\sqrt{2} x^2+5 x+\sqrt{2}=0$ find the value of the discriminant.
- A
$-5$
- ✓
$17$
- C
$2$
- D
$2 \sqrt{2}-5$
Answer$\sqrt{2} x^2+5 x+\sqrt{2}=0$ compare with $a x^2+b x+c=0$
$\Rightarrow a=\sqrt{2}, b=5 \text { and } c=\sqrt{2} $
$\therefore b ^2-4 ac =5^2-4(\sqrt{2})(\sqrt{2})$
$=25-8$
$=17$
View full question & answer→MCQ 61 Mark
Choose the correct answer for the following question.
The roots of $x^2+k x+k=0$ are real and equal, find k.
AnswerCorrect option: C. $0$ or $4$
$x ^2+ kx + k =0$, equation has real and equal roots.
$\therefore b ^2-4 ac =0 $
$\Rightarrow k ^2-4(1) k =0 $
$\Rightarrow k ( k -4)=0 $
$k =0 \text { or } k -4=0 \Rightarrow k =4 $
$\therefore k =0 \text { or } 4$
View full question & answer→MCQ 71 Mark
Choose the correct answer for the following question.
Out of the following equations which one is not a quadratic equation?
- ✓
$x^2 + 4x = 11 + x^2$
- B
$5x^2 = 90$
- C
$x^2 = 4x$
- D
$2x – x^2 = x^2 + 5$
AnswerCorrect option: A. $x^2 + 4x = 11 + x^2$
$x^2+4 x-11-x^2=0 \Rightarrow 4 x-11=0$
In all other options highest degree of equation is 2, which also the degree of quadratic equation. But in Option A, degree of polynomial is 1
View full question & answer→Question 81 Mark
Choose the correct answer for the following question.
Which one is the quadratic equation?
A.$\frac{5}{x}-3=x^2$
B. $x(x+5)=2$
C. $n-1=2 n$
D.$\frac{1}{x^2}(x+2)=x$
AnswerIn option $A \frac{5}{x}-3=x^2 \Rightarrow 5-3 x=x^3$. hence, it is not a quadratic equation.
In Option $B x ( x +5)=2 \Rightarrow x ^2+5 x -2=0$, it is a quadratic equation.
In Option $C n -1=2 n \Rightarrow 2 n - n =-1 \Rightarrow n =-1$, it is not a quadratic equation.
In Option $D \frac{1}{ x ^2}( x +2)= x \Rightarrow x +2= x ^3$, hence, it is not a quadratic equation.
View full question & answer→MCQ 91 Mark
If one root of quadratic equation is $5+\sqrt{5}$, then the product of roots is ______ .
View full question & answer→MCQ 101 Mark
$\alpha^3+\beta^3=$ _____ .
- ✓
$(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
- B
$(\alpha-\beta)^3+3 \alpha \beta(\alpha-\beta)$
- C
$(\alpha+\beta)^3-3 \alpha \beta(\alpha-\beta)$
- D
$(\alpha-\beta)^3-3 \alpha \beta(\alpha-\beta)$
AnswerCorrect option: A. $(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
$(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
View full question & answer→MCQ 111 Mark
The product of the roots $(\alpha \times \beta)=$ ______ .
- A
$\frac{-b}{a}$
- B
$\frac{-c}{a}$
- C
$\frac{b}{a}$
- ✓
$\frac{c}{a}$
AnswerCorrect option: D. $\frac{c}{a}$
$\frac{c}{a}$
View full question & answer→MCQ 121 Mark
Which of the following is not a quadratic equation?
- A
$\frac{-5}{3} x^2=2 x+9$
- B
$(x+3)(x+4)$
- ✓
$\frac{5}{x}-3=x^2$
- D
$\frac{7}{m}=3 m+5$
AnswerCorrect option: C. $\frac{5}{x}-3=x^2$
$\frac{5}{x}-3=x^2$
View full question & answer→MCQ 131 Mark
Three times the square of natural number is 363 is written in the mathematical equation form as ________ .
- A
$x^2+3=363$
- B
$x^2-3=363$
- ✓
$3 x^2=363$
- D
$\frac{x^2}{3}=363$
AnswerCorrect option: C. $3 x^2=363$
$3 x^2=363$
View full question & answer→MCQ 141 Mark
What is the nature of roots of quadratic equation $9 x^2-12 x+4=0$ ?
View full question & answer→MCQ 151 Mark
The standard form of quadratic equation $x-\frac{5}{x}=3 x-7$ is _____ .
- A
$2 x^2-8 x+7=0$
- B
$2 x^2+7 x+5=0$
- ✓
$2 x^2-7 x+5=0$
- D
$2 x^2-5 x+7=0$
AnswerCorrect option: C. $2 x^2-7 x+5=0$
$2 x^2-7 x+5=0$
View full question & answer→MCQ 161 Mark
In a quadratic equation, $\alpha+\beta=-4$ and $\alpha \beta=-1$, then required equation is ______ .
- A
$x^2-4 x-1=0$
- ✓
$x^2+4 x-1=0$
- C
$x^2+4 x+1=0$
- D
$x^2-4 x+1=0$
AnswerCorrect option: B. $x^2+4 x-1=0$
$x^2+4 x-1=0$
View full question & answer→MCQ 171 Mark
The value of discriminant of the equation $x^2+x+1=0$ is ______ .
View full question & answer→MCQ 181 Mark
It the roots of $a x^2+b x+c=0$ are real and equal then ______ .
- A
$b^2-4 a c<0$
- ✓
$b^2-4 a c=0$
- C
$b^2-4 a c>0$
- D
AnswerCorrect option: B. $b^2-4 a c=0$
$b^2-4 a c=0$
View full question & answer→MCQ 191 Mark
If one root of quadratic equation is $1-\sqrt{3}$ then the other root is ______ .
- A
$1-\sqrt{3}$
- B
$-1-\sqrt{3}$
- C
$1+2 \sqrt{3}$
- ✓
$1+\sqrt{3}$
AnswerCorrect option: D. $1+\sqrt{3}$
$1+\sqrt{3}$
View full question & answer→MCQ 201 Mark
If one root of quadratic equation $k x^2-7 x+12=0$ is 3 , then value of $k$ is ______ .
View full question & answer→MCQ 211 Mark
If the roots of a quadratic equation are real and equal, then $\Delta$ must be
View full question & answer→MCQ 221 Mark
The roots of a quadratic equation $y^2-16 y+63=0$ are ______ .
View full question & answer→MCQ 231 Mark
The sum of roots $(\alpha+\beta)=$ _______ .
- ✓
$\frac{-b}{a}$
- B
$\frac{b}{a}$
- C
$\frac{-c}{a}$
- D
$\frac{c}{a}$
AnswerCorrect option: A. $\frac{-b}{a}$
$\frac{-b}{a}$
View full question & answer→MCQ 241 Mark
Answer
$\begin{array}{l}\sqrt{5} m ^2+\sqrt{5} m +\sqrt{5}=0 \text { compare with } ax ^2+ bx + c =0 \\ \Rightarrow a =\sqrt{5}, b =\sqrt{5} \text { and } c =\sqrt{5} \\ \therefore b ^2-4 ac =\sqrt{5}^2-4(\sqrt{5})(\sqrt{5}) \\ =5-20 \\ =-15 \\ \therefore b ^2-4 ac <0 \text {.hence, roots are not real. }\end{array}$
View full question & answer→MCQ 251 Mark
Out of the following equations, find the equation having the sum of its roots -5.
AnswerSum of the roots i.e. $\alpha+\beta=-\frac{b}{a}$
$\therefore$ in option $A , \alpha+\beta=-\frac{-15}{3}=5$
$\therefore$ in option $B, {\alpha+\beta}=-\frac{-5}{1}=5$
$\therefore$ in option $A, \alpha+\beta=-\frac{3}{1}=3$
$\therefore$ in option $A ,{\alpha+\beta}=-\frac{15}{3}=-5$
View full question & answer→MCQ 261 Mark
Which of the following quadratic equations has roots 3, 5?
Answer(B) $x^2-8 x+15=0$
$\begin{array}{l}
x^2-8 x+15=0 \\
\Rightarrow x^2-5 x-3 x+15=0 \\
\Rightarrow x(x-5)-3(x-5)=0 \\
\Rightarrow(x-5)(x-3)=0
\end{array}$
$\begin{array}{l}
\Rightarrow x-5=0 \text { or } x-3=0 \\
x=5 \text { and } x=3
\end{array}$
View full question & answer→MCQ 271 Mark
For $\sqrt{2} x^2-5 x+\sqrt{2}=0$ find the value of the discriminant.
Answer(B) 17
$\begin{array}{l}\sqrt{2} x^2+5 x+\sqrt{2}=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=\sqrt{2}, b=5 \text { and } c=\sqrt{2} \\ \therefore b^2-4 a c=5^2-4(\sqrt{2})(\sqrt{2}) \\ =25-8 \\ =17\end{array}$
View full question & answer→MCQ 281 Mark
The roots of x2 + kx + k = 0 are real and equal, find k.
Answer$x ^2+ kx + k =0$, equation has real and equal roots.
$\therefore b ^2-4 ac =0$
$\Rightarrow k ^2-4(1) k =0$
$\Rightarrow k ( k -4)=0$
$k =0$ or $k -4=0 \Rightarrow k =4$
$\therefore k =0$ or 4
View full question & answer→MCQ 291 Mark
Out of the following equations which one is not a quadratic equation?
Answer$x^2+4 x-11-x^2=0 \Rightarrow 4 x-11=0$
In all other options highest degree of equation is 2, which also the degree of quadratic equation. But in Option A, degree of polynomial is 1
View full question & answer→MCQ 301 Mark
One of the roots of equation $x^2+m x-5=0$ is 2 ; find $m$.
- A
- B
$-\frac{1}{2}$
- C
$\frac{1}{2}$
- D
View full question & answer→MCQ 311 Mark
Which one is the quadratic equation?
- A
$\frac{5}{x}-3=x^2$
- B
$x(x+5)=2$
- C
$n-1=2 n$
- D
$\frac{1}{x^2}(x+2)=x$
AnswerIn option $A \frac{5}{x}-3=x^2 \Rightarrow 5-3 x=x^3$. hence, it is not a quadratic equation.
In Option $B x(x+5)=2 \Rightarrow x^2+5 x-2=0$, it is a quadratic equation.
In Option $C n -1=2 n \Rightarrow 2 n - n =-1 \Rightarrow n =-1$, it is not a quadratic equation.
In Option $D \frac{1}{x^2}(x+2)=x \Rightarrow x+2=x^3$, hence, it is not a quadratic equation.
View full question & answer→MCQ 321 Mark
Which of the following is not a quadratic equation?
- A
$\frac{-5}{3} x^2=2 x+9$
- B
$(x+3)(x+4)$
- ✓
$\frac{5}{x}-3=x^2$
- D
$\frac{7}{m}=3 m+5$
AnswerCorrect option: C. $\frac{5}{x}-3=x^2$
$\frac{5}{x}-3=x^2$
View full question & answer→MCQ 331 Mark
What is the nature of roots of quadratic equation $9 x^2-12 x+4=0$ ?
View full question & answer→MCQ 341 Mark
Three times the square of natural number is 363 is written in the mathematical equation form as ________ .
- A
$x^2+3=363$
- B
$x^2-3=363$
- ✓
$3 x^2=363$
- D
$\frac{x^2}{3}=363$
AnswerCorrect option: C. $3 x^2=363$
$3 x^2=363$
View full question & answer→MCQ 351 Mark
The value of discriminant of the equation $x^2+x+1=0$ is ______ .
View full question & answer→MCQ 361 Mark
The sum of roots $(\alpha+\beta)=$ _______ .
- ✓
$\frac{-b}{a}$
- B
$\frac{b}{a}$
- C
$\frac{-c}{a}$
- D
$\frac{c}{a}$
AnswerCorrect option: A. $\frac{-b}{a}$
$\frac{-b}{a}$
View full question & answer→MCQ 371 Mark
The standard form of quadratic equation $x-\frac{5}{x}=3 x-7$ is _____ .
- A
$2 x^2-8 x+7=0$
- B
$2 x^2+7 x+5=0$
- ✓
$2 x^2-7 x+5=0$
- D
$2 x^2-5 x+7=0$
AnswerCorrect option: C. $2 x^2-7 x+5=0$
$2 x^2-7 x+5=0$
View full question & answer→MCQ 381 Mark
The roots of a quadratic equation $y^2-16 y+63=0$ are ______ .
View full question & answer→MCQ 391 Mark
The product of the roots $(\alpha \times \beta)=$ ______ .
- A
$\frac{-b}{a}$
- B
$\frac{-c}{a}$
- C
$\frac{b}{a}$
- ✓
$\frac{c}{a}$
AnswerCorrect option: D. $\frac{c}{a}$
$\frac{c}{a}$
View full question & answer→MCQ 401 Mark
It the roots of $a x^2+b x+c=0$ are real and equal then ______ .
- A
$b^2-4 a c<0$
- ✓
$b^2-4 a c=0$
- C
$b^2-4 a c>0$
- D
AnswerCorrect option: B. $b^2-4 a c=0$
$b^2-4 a c=0$
View full question & answer→MCQ 411 Mark
In a quadratic equation, $\alpha+\beta=-4$ and $\alpha \beta=-1$, then required equation is ______ .
- A
$x^2-4 x-1=0$
- ✓
$x^2+4 x-1=0$
- C
$x^2+4 x+1=0$
- D
$x^2-4 x+1=0$
AnswerCorrect option: B. $x^2+4 x-1=0$
$x^2+4 x-1=0$
View full question & answer→MCQ 421 Mark
If the roots of a quadratic equation are real and equal, then $\Delta$ must be
View full question & answer→MCQ 431 Mark
If one root of quadratic equation $k x^2-7 x+12=0$ is 3 , then value of $k$ is ______ .
View full question & answer→MCQ 441 Mark
If one root of quadratic equation is $5+\sqrt{5}$, then the product of roots is ______ .
View full question & answer→MCQ 451 Mark
If one root of quadratic equation is $1-\sqrt{3}$ then the other root is ______ .
- A
$1-\sqrt{3}$
- B
$-1-\sqrt{3}$
- C
$1+2 \sqrt{3}$
- ✓
$1+\sqrt{3}$
AnswerCorrect option: D. $1+\sqrt{3}$
$1+\sqrt{3}$
View full question & answer→MCQ 461 Mark
$\alpha^3+\beta^3=$ _____ .
- ✓
$(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
- B
$(\alpha-\beta)^3+3 \alpha \beta(\alpha-\beta)$
- C
$(\alpha+\beta)^3-3 \alpha \beta(\alpha-\beta)$
- D
$(\alpha-\beta)^3-3 \alpha \beta(\alpha-\beta)$
AnswerCorrect option: A. $(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
$(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$
View full question & answer→