SOLUTION: Prove that if one root of the equation ax^2-bx+c=0 is twice the other then alpha=2b^2/9c

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Question 1056915: Prove that if one root of the equation ax^2-bx+c=0 is twice the other then alpha=2b^2/9c
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
You did not say how you decided to pick "alpha".

The two roots generally are x=%28b-sqrt%28%28-b%29%5E2-4ac%29%29%2F2a and x=%28b%2Bsqrt%28%28-b%29%5E2-4ac%29%29%2F2a.

system%28x=%28b-sqrt%28b%5E2-4ac%29%29%2F2a%2Cx=%28b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29%29

Take the PLUS form to be as described, twice the other, then
2%28b-sqrt%28b%5E2-4ac%29%29=b%2Bsqrt%28b%5E2-4ac%29
Work with that in the way most important or useful for you.