SOLUTION: Derive a quadratic equation using: x= [-6 +- (5 sqrt 2)]/ 3

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Question 766506: Derive a quadratic equation using: x= [-6 +- (5 sqrt 2)]/ 3
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
Derive a quadratic equation using: x= %28-6+%2B-+5sqrt%282%29%29%2F3.
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A:
The sum of the roots is %28-6+%2B+5sqrt%282%29%29%2F3 + %28-6+-+5sqrt%282%29%29%2F3 = -4.
The product of the roots is %28%28-6+%2B+5sqrt%282%29%29%2F3%29%28%28-6+-+5sqrt%282%29%29%2F3%29 = %2836+-+50%29%2F9 = -14%2F9.
The quadratic equation is x%5E2 - (sum of roots)x + (product of roots) = 0.
x%5E2+%2B+4x+-+14%2F9+=+0, multiply both sides by 9.
ANSWER: highlight%289x%5E2+%2B+36x+-+14+=+0%29