SOLUTION: Form a quadratic equations whose roots are 1+ sqrt2 and 1 - sqrt 2.

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Question 1128592: Form a quadratic equations whose roots are 1+ sqrt2 and 1 - sqrt 2.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Form a quadratic equations whose roots are 1+ sqrt2 and 1 - sqrt 2.
:
x = 1 +/-sqrt%282%29
x - 1 = +/-sqrt%282%29
square both side
(x+1)^2 = 2
FOIL (x-1)(x-1)
x^2 - 2x + 1 = 2
x^2 - 2x + 1 - 2 = 0
then
y = x^2 - 2x - 1 = 0 is the quadratic equation

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Form a quadratic highlight%28cross%28equations%29%29 equation whose roots are 1+ sqrt2 and 1 - sqrt 2.
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Use the Vieta's theorem.



The product of the roots is the constant term of the polynomial:

    %281%2Bsqrt%282%29%29%2A%281-sqrt%282%29%29 = 1%5E2+-+%28sqrt%282%29%29%5E2 = 1 - 2 = -1.



The sum of the root is equal to %281%2Bsqrt%282%29%29%2A%281-sqrt%282%29%29 = 2,

and it is the coefficient at x taken with the opposite sign.

Hence, the coefficient at x is equal to -2.



Then the equation is  x%5E2+-2x+-1 = 0.