Solve the following quadratic equation:4x^2 - 2(a^2 + b^2)x + a^2… - Vidyadip

Question

Solve the following quadratic equation:$4x^2 - 2(a^2 + b^2)x + a^2b^2 = 0$

✓

Answer

$4x^2 - 2(a^2 + b^2)x + a^2b^2 = 0$
$\Rightarrow 4x^2 - 2a^2x - 2b^2x + a^2b^2 = 0$
$\Rightarrow 2x(2x - a^2) - b^2(2x - a^2) = 0$
$\Rightarrow (2x - a^2)(2x - b^2) = 0$
$\Rightarrow (2x - a^2) = 0 or (2x - b^2) = 0$
$\Rightarrow\text{x}=\frac{\text{a}^2}{\text{2}}$ or $\text{x}=\frac{\text{b}^2}{\text{2}}$
Hence, $\frac{\text{a}^2}{\text{2}}$ and $\frac{\text{b}^2}{\text{2}}$ are the roots of the given equation.

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 "5 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Solve 2x + 3y = 11 and 2x – 4y = –24 and hence find the value of m for which y = mx + 3.

Calculate the mean of the following frequency distribution:

Class:	10-30	30-50	50-70	70-90	90-110	110-130
Frequency:	5	8	12	20	3	2

A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20m. The heights of the cylindrical and conical portions are 4.2m and 2.1m respectively. Find the volume of the tent.

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80m wide. From a point P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Find the height of each pole and distances of the point P from the poles.

Construct an isosceles triangle whose base is 9cm and altitude 5cm. Construct another triangle whose side are $\frac34$ of the corresponding sides of the first isosceles triangle.

How many numbers are there between 101 and 999, which are divisible by both 2 and 5?

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

The dimensions of a room are 14m × 10m × 6.5m. There are two doors and 4 windows in the room. Each door measures 2.5m × 1.2m and each window measures 1.5m × 1m. Find the cost of painting the four walls of the room at ₹ 35 per $m^2.$