SOLUTION: The equation x^2-2x-11=0 has solutions a and b. Find the value of a^2 + b^2. Please help me and give explanation in detail so I can understand it. Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The equation x^2-2x-11=0 has solutions a and b. Find the value of a^2 + b^2. Please help me and give explanation in detail so I can understand it. Thank you!      Log On


   

Question 767458: The equation x^2-2x-11=0 has solutions a and b. Find the value of a^2 + b^2.
Please help me and give explanation in detail so I can understand it. Thank you!
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
The equation x%5E2-2x-11=0 has solutions a and b. Find the value of a%5E2+%2B+b%5E2.
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The sum of the roots of a quadratic equation Ax%5E2+%2B+Bx+%2B+C+=+0 is equal to %28-B%29%2FA and the product of the roots is equal to C%2FA.
In x%5E2-2x-11=0, a + b = %28-%28-2%29%29%2F1 = 2 and ab = %28-11%29%2F1 = -11.
%28a+%2B+b%29%5E2 = a%5E2+%2B+2ab+%2B+b%5E2
so a%5E2+%2B+b%5E2 = %28a%2Bb%29%5E2+-+2ab = 2%5E2+-+2%28-11%29 = highlight%2826%29.
ANSWER: highlight%2826%29