document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #769286 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "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.

\n" ); document.write( "So in this problem the sum of the roots is -5.

\n" ); document.write( "But the sum of the roots is w + 2w + w+3. So

\n" ); document.write( " $\"w%2B2w%2Bw%2B3+=+-5\"$
\n" ); document.write( " $\"4w+=+-8\"$
\n" ); document.write( " $\"w+=+-2\"$

\n" ); document.write( "So the roots of the polynomial are -2, -4, and 1. And then the polynomial is

\n" ); document.write( " $\"%28x%2B2%29%28x%2B4%29%28x-1%29+=+%28x%5E2%2B6x%2B8%29%28x-1%29+=+x%5E3%2B5x%5E2%2B2x-8\"$

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