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Prove that if 2a^3 + 27c = 9ab, then the roots of x^3 + ax^2 + bx + c = 0 form an arithmetic sequence.

 Feb 2, 2020
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You can take a = b = c = 0.  Then the cubic becomes x^3 = 0.  The roots are 0, 0, 0, which is an arithmetic sequence.

 Feb 3, 2020

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