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: 4 x 2 – 4a 2 x + (a 4 – b 4 ) = 0

Philoid · Accepted Answer

Given: 4x² – 4a²x + (a⁴ – b⁴) = 0

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

A = 4, B = – 4a², C = (a⁴ – b⁴)

Discriminant D = B² – 4AC

= (– 4a²)² – 4.4. (a⁴ – b⁴)

= 16a⁴ + 16b⁴ – 16a⁴ = 16 b⁴ > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are