How do you find all the zeros of F(x) = x^4 - 13x^2 + 36F(x)=x4−13x2+36?
1 Answer
Jul 16, 2016
Zeros:
Explanation:
Since there are no terms of odd degree, we can treat this as a quadratic in
First note that
x^4-13x^2+36x4−13x2+36
=(x^2)^2-13(x^2)+36=(x2)2−13(x2)+36
=(x^2-9)(x^2-4)=(x2−9)(x2−4)
=(x^2-3^2)(x^2-2^2)=(x2−32)(x2−22)
=(x-3)(x+3)(x-2)(x+2)=(x−3)(x+3)(x−2)(x+2)
Hence zeros:
+-3±3 ,+-2±2