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Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
3a2x2 + 8abx + 4b2 = 0, a ≠ 0
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 – 4.3a2. 4b2
= 64 a2b2 – 48a2b2 = 16a2b2 > 0
Hence the roots of equation are real.
Roots are given by
Hence the roots of equation are