SOLUTION: If x³+3ax²+bx+c is a perfect cube, prove that b³=27c².
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Question 1108050: If x³+3ax²+bx+c is a perfect cube, prove that b³=27c².
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
In a polynomial of degree n, the sum of the roots is -b/a, where a is the leading coefficient and b is the coefficient of the degree (n-1) term.
In this problem, the sum of the roots is therefore .
If the polynomial is a perfect cube, and the sum of the roots is -3a, then each root is -a, and the polynomial is
So the coefficient of x is , and the constant is .
And then
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