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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.

Hint: For part (b), let $y = x + \frac{a}{3}$ and rewrite $x^3 + ax^2 + bx + c = 0$ in terms of y

 Mar 14, 2020
edited by Guest  Mar 14, 2020
edited by Guest  Mar 14, 2020
edited by Guest  Mar 14, 2020
edited by Guest  Mar 14, 2020
 #1
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First, you can check if its true for a = b = c = 0, because then all the roots are 0.

 May 22, 2020

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