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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. 

 Jun 17, 2020
 #1
avatar+30673 
+3

Here's (a):

 

Now see if you can do (b).

 Jun 17, 2020

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