(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
form an arithmetic sequence.
Here's (a):
Now see if you can do (b).
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