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If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 - 3abc + a2d = 0

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Let α = A - D, β = A and y = A + D are the zeros of the given polynomial.

Sum of the zeros

Since A is the zero of the polynomial,

therefore f(A) = 0

On substitution A = - \(\frac{b}{a}\), we get

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