Find the roots of

Given: 12abx² – (9a² – 8b²)x – 6ab = 0

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

A = 12ab, B = – (9a² – 8b²), C = – 6ab

Discriminant D = B² – 4AC

= [ – (9a² – 8b²)]² – 4.12ab. – 6ab

= 81a⁴ – 144a²b² + 64b⁴ + 288 a²b²

= 81a⁴ + 144a²b² + 64b⁴

= (9a² + 8b²)² > 0 Using a² + 2ab + b² = (a + b)²

Hence the roots of equation are real.

= 9a² + 8b²

Roots are given by

Hence the roots of equation are