SOLUTION: Hello me and my friend are having trouble finding the zeros of a polynomial function P(x)=2x(x^2+9)(x^2-2) we foiled everything out to P(x)=x^4+7x^2+2x-18 and then we trie

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello me and my friend are having trouble finding the zeros of a polynomial function P(x)=2x(x^2+9)(x^2-2) we foiled everything out to P(x)=x^4+7x^2+2x-18 and then we trie      Log On


   

Question 671593: Hello me and my friend are having trouble finding the zeros of a polynomial function
P(x)=2x(x^2+9)(x^2-2)
we foiled everything out to P(x)=x^4+7x^2+2x-18
and then we tried finding our P/Q and using synthetic division to get a zero, but we couldn't get the right answer. The answer is supposed to be 0,+-sqrt(2)
Thanks in advance for the help.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=2x%28x%5E2%2B9%29%28x%5E2-2%29
2x%28+x%5E4%2B7x%5E2-18%29

2x%28+x%5E4%2B7x%5E2%2B%2849%2F4%29+-49%2F4-18%29=0

2x%28%28x%5E2%2B%287%2F2%29%29%5E2-%28%2849%2B72%29%2F2%29%29=0

%282x%28x%5E2%2B%287%2F2%29%29%5E2-%28121%2F2%29%29=0
%28x%5E2%2B%287%2F2%29%29%5E2=%28121%2F2%29

take the square root
x^2+(7/2) = +-(11/2)
x^2= (11/2)-(7/2) OR (-11/2)-(7/2)
x^2=2 OR -9
x=sqrt(2),-sqrt(2), 0, 3i