How do you find all the zeros of F(x)=x413x2+36?

1 Answer
Jul 16, 2016

Zeros: ±3, ±2

Explanation:

Since there are no terms of odd degree, we can treat this as a quadratic in x2 to simplify it, then factorize each of the resulting quadratic factors.

First note that 36=9×4 and 9+4=13, so we find:

x413x2+36

=(x2)213(x2)+36

=(x29)(x24)

=(x232)(x222)

=(x3)(x+3)(x2)(x+2)

Hence zeros:

±3, ±2