Solve the following quadratic equation using formula method only … - Vidyadip

Question

Solve the following quadratic equation using formula method only
$\frac{5}{4} x^2-2 \sqrt{5} x+4=0$

✓

Answer

$\frac{5}{4} x^2-2 \sqrt{5} x+4=0$
$ 5 x^2-8 \sqrt{5} x+16=0$
$ a=5 ; b=-8 \sqrt{5} ; c=16$
$D=b^2-4 a c$
$ =(-8 \sqrt{5})^2-4(5)(15)$
$ =40-300 \\ =-260$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a} $
$ x=\frac{-(-8 \sqrt{5}) \pm \sqrt{-260}}{2 \times 5} $
$ x=\frac{8 \sqrt{5} \pm \sqrt{-260}}{2 \times 5}$
$ x=\frac{4 \sqrt{5}}{5} \quad \text { (Since } \sqrt{-260} \text { is not possible) }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Quadratic Equations→Quadratic Equations — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

The angle of elevation of a stationary cloud from a point 25m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level?

If $a: b=c: d$, then prove that $\frac{a^2+c^2}{b^2+d^2}=\frac{a c}{b c}$

In an A.P, the first term is $25,$ nth term is $-17$ and the sum of n terms is $132.$ Find n and the common difference.

Prove that the points $(7 , 10) , (-2 , 5)$ and $(3 , -4)$ are vertices of an isosceles right angled triangle.

Anand bought an Almirah for $Rs. 5,135.70$ which included $15\%$ rebate on the basic price and then $6\%$ sales tax on the remaining price. Find the basic price of the almirah.

Prove that the line segment joining the midpoints of two parallel chords of a circle passes through its centre.

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

If $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$, prove that
$
\frac{3 x^3-5 y^3+4 c^3}{3 a^3-5 b^3+4 c^3}=\left(\frac{3 x-5 y+4 c}{3 a-5 b+a c}\right)^3
$

Find the sum invested at $8\%$ p.a. compound interest on which the interest for the third year exceeds that of the first year by $Rs. 166.40.$

The points $P (1,-1 ), Q ( 4,-1)$ and $R ( 4, 3)$ are reflected in $y-$axis. If the images are denoted by $P' , Q'$ , and $R'$ , then
$(i)$ Find the co$-$ordinates of $P'Q'R' , Q'$ and $R'$
$(ii)$ What kind of figure is formed by $RR' Q' Q? $
$(iii)$ Find the perimeter of the figure $P'Q'R'$