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

Question

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: x 2 – 4ax – b 2 + 4a 2 = 0

Philoid · Accepted Answer

Given: x² – 4ax – b² + 4a² = 0

Comparing with standard quadratic equation Ax² + Bx + C = 0

A = 1, B = – 4a, C = – b² + 4a²

Discriminant D = B² – 4AC

= (– 4a)²– 4.1. (– b² + 4a²)

= 16a² + 4b² – 16a² = 4 b² > 0

Hence the roots of equation are real.

Roots are given by

x = (2a – b) or x = (2a + b)

Hence the roots of equation are (2a – b) or (2a + b)