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Question

Let a, b, c be distinct complex numbers such that aligned 2a^3 + 7a^2 - 8a + 5 &= 0, 2b^3 + 7b^2 - 8b + 5 &= 0, 2c^3 + 7c^2 - 8c + 5 &= 0. alignedCompute the value of the product abc.

Accepted Answer

We are given that the roots of the polynomial equation 2x^3 + 7x^2 - 8x + 5 = 0are a, b, c (because they all satisfy the equation). Therefore, by Vieta's formulas, abc = -52.