SOLUTION: Find all quartic polynomials with zeros of: +-1 , +- {{{sqrt(2)}}} Thank you :)

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Question 394728: Find all quartic polynomials with zeros of:
+-1 , +- sqrt%282%29
Thank you :)
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"Find all quartic polynomials with zeros of:
+-1 , +- sqrt%282%29
Thank you :)"

Hope following helps:
find all the binomials that add to 0 and multiply to the quadnomial set to 0 that is needed
(x + 1)(x - 1)(x - sqrt%282%29)(x + sqrt%282%29) = 0 this has the zeros you said above
multiply and use FOIL (First Outer Inner Last) and distribution
(x^2 - 1)(x^2 - 2) = 0 when you got a plus and a minus the middle terms cancel out
x^4 - 2x^2 - x^2 + 2 = 0
x^4 - 3x^2 + 2 = 0
check with 1 and sqrt%282%29:
1 - 3 + 2 = -2 + 2 = 0, yes
4 - 6 + 2 = -2 + 2 = 0, yes