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)   (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 +/-
x - 1 = +/-
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)   (Show Source): You can put this solution on YOUR website!
.
Form a quadratic equation whose roots are 1+ sqrt2 and 1 - sqrt 2.
~~~~~~~~~~~~~~~~~~~ 


Use the Vieta's theorem.



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

     =  = 1 - 2 = -1.



The sum of the root is equal to  = 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   = 0.


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