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Question

3a2x2+8abx+4b2=0, a0

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Solution

Given:3a2x2 + 8abx + 4b2 = 0 On comparing it with Ax2 + Bx + C = 0, we get:A = 3a2, B = 8ab and C = 4b2 Discriminant D is given by:D = (B2 4AC) = (8ab)2 4 × 3a2 × 4b2 = 16a2b2 > 0Hence, the roots of the equation are real.Roots α and β are given by:α = b + D2a = 8ab + 16a2b22 × 3a2 = 8ab + 4ab6a2 = 4ab6a2 = 2b3aβ = b D2a = 8ab 16a2b22 × 3a2 = 8ab 4ab6a2 = 12ab6a2 = 2baThus, the roots of the equation are 2b3a and 2ba.

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