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: 3a 2 x 2 + 8abx + 4b 2 = 0, a ≠ 0

Philoid · Accepted Answer

Given: 3a²x² + 8abx + 4b² = 0

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

A = 3a², B = 8ab, C = 4b²

Discriminant D = B² – 4AC

= (8ab)² – 4.3a^2. 4b²

= 64 a²b² – 48a²b² = 16a²b² > 0

Hence the roots of equation are real.

= 4ab

Roots are given by

Hence the roots of equation are