SOLUTION: if the ratio of the roots of the equation x^3+5x^2+px+q=0 are w, 2w, and w+3, find the values of w, p, and q

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Question 1147956: if the ratio of the roots of the equation x^3+5x^2+px+q=0 are w, 2w, and w+3, find the values of w, p, and q
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the roots of a polynomial equation of degree n is -b/a, where a is the leading coefficient (of the x^n term) and b is the coefficient of the x^(n-1) term.

So in this problem the sum of the roots is -5.

But the sum of the roots is w + 2w + w+3. So

w%2B2w%2Bw%2B3+=+-5
4w+=+-8
w+=+-2

So the roots of the polynomial are -2, -4, and 1. And then the polynomial is

%28x%2B2%29%28x%2B4%29%28x-1%29+=+%28x%5E2%2B6x%2B8%29%28x-1%29+=+x%5E3%2B5x%5E2%2B2x-8