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: 36x 2 – 12ax + (a 2 – b 2 ) = 0

Philoid · Accepted Answer

Given: 36x² – 12ax + (a² – b²) = 0

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

A = 36, B = – 12a, C = a² – b²

Discriminant D = B² – 4AC

= (– 12a)² – 4.36.(a² – b²)

= 144a² – 144a² + 144 b² = 144 b² > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are