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 – 2ax – (4b 2 – a 2 ) = 0

Philoid · Accepted Answer

Given: x² – 2ax – (4b² – a²) = 0

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

A = 1, B = – 2a, C = – (4b² – a²)

Discriminant D = B² – 4AC

= (– 2a)² – 4.1. – (4b² – a²)

= 4a² – 4a² + 16 b² = 16b² > 0

Hence the roots of equation are real.

Roots are given by

x = (a + 2b) or x = (a – 2b)

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