SOLUTION: Find a polynomial with the given zeros. 1, -1, square root of 2, negative square root of 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial with the given zeros. 1, -1, square root of 2, negative square root of 2      Log On


   

Question 167736: Find a polynomial with the given zeros.
1, -1, square root of 2, negative square root of 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Since 1, -1, sqrt%282%29, and -sqrt%282%29 are given zeros this means that:


x=1, x=-1, x=sqrt%282%29, and x=-sqrt%282%29


Squaring both sides of the last two equations gets: x%5E2=2 and x%5E2=2


So we really have 3 equations x=1, x=-1, and x%5E2=2


Get all terms to the left side in each case


x-1=0, x%2B1=0, and x%5E2-2=0


Now use the zero product property in reverse to join the factors.


%28x-1%29%28x%2B1%29%28x%5E2-2%29=0


FOIL %28x-1%29%28x%2B1%29 to get x%5E2-1

%28x%5E2-1%29%28x%5E2-2%29=0


x%5E4-3x%5E2%2B2=0 FOIL


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Answer:

So the polynomial with roots of 1, -1, sqrt%282%29, and -sqrt%282%29 is

y=x%5E4-3x%5E2%2B2