SOLUTION: If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value of α^3+ β ^3 is:

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Question 972973: If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value of α^3+ β ^3 is:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value of α^3+ β ^3 is:
Solution:
The sum of the roots of the equation ax%5E2%2Bbx%2Bc+=+0 is -b%2Fa and the product of the roots is c%2Fa.
%28alpha%29%5E3+%2B+%28beta%29%5E3 = %28%28alpha%29%2B%28beta%29%29%28%28alpha%29%5E2-%28alpha%29%28beta%29%2B%28beta%29%5E2%29 = %28-b%2Fa%29%28%28alpha%29%5E2%2B%28beta%29%5E2-c%2Fa%29
But %28alpha%29%5E2%2B%28beta%29%5E2 = %28%28alpha%29+%2B+%28beta%29%29%5E2+-+2%28alpha%29%28beta%29
= %28-b%2Fa%29%5E2+-+2%28c%2Fa%29
Therefore,
%28alpha%29%5E3+%2B+%28beta%29%5E3 = %28-b%2Fa%29%28%28-b%2Fa%29%5E2+-+2%28c%2Fa%29-c%2Fa%29
= highlight%28%28-b%2Fa%29%28%28-b%2Fa%29%5E2+-+3%28c%2Fa%29%29%29