SOLUTION: One of the roots of the quadratic equation ax2+bx+c=0 is twice the other.Show that 2b2=9ac

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Question 536504: One of the roots of the quadratic equation ax2+bx+c=0 is twice the other.Show that 2b2=9ac
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let r and 2r be the roots. By Vieta's formulas, the sum of the roots is -b/a and the product of the roots is c/a. We have





Squaring the first equation,



This is equal to c/a so we have

This can be simplified and rearranged to obtain 2b^2 = 9ac.