# Find the roots of each of the following equations, if they exist, by applying the quadratic formula:12abx2 – (9a2 – 8b2)x – 6ab = 0, where a ≠ 0 and b ≠ 0

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

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