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

(b) Prove that if $2a^3 + 27c = 9ab,$ then the roots of \[x^3 + ax^2 + bx + c = 0\]form an arithmetic sequence.

 Sep 2, 2020
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If a = b = c = 0, then all the roots are 0.

 Sep 2, 2020

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