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 + 4bx – (a 2 – b 2 ) = 0

Philoid · Accepted Answer

Given: 4x² + 4bx – (a² – b²) = 0

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

A = 4, B = 4b, C = – (a² – b²)

Discriminant D = B² – 4AC

= (4b)² – 4.4. – (a² – b²)

= 16b² + 16a² – 16b² = 16 a² > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are