Question

Find the roots of the following equations, if they exist, by applying the quadratic formula:

x² - 2ax + (a² - b²) = 0

Answer 1

Given

x² - 2ax + (a² - b²) = 0

On Comparing it with Ax² + Bx + C = 0.we get

A = 1,B = -2a and C = (a² - b²)

Discriminant D is given by:

D = B² - 4AC

=(-2a)² - 4 x 1 x (a² - b²)

= 4a² - 4a² + 4b²

= 4b² > 0

Hence, the roots of the equation are real.

Roots α and β are given by:

Hence, the roots of the equation are (a + b) and (a - b).