Question

How do you find all the zeros of `F(x) = x^4 - 13x^2 + 36`?

Answer 1

Zeros: `+-3`, `+-2`

Explanation:

Since there are no terms of odd degree, we can treat this as a quadratic in `x^2` to simplify it, then factorize each of the resulting quadratic factors.

First note that `36 = 9xx4` and `9+4=13`, so we find:

`x^4-13x^2+36`

`=(x^2)^2-13(x^2)+36`

`=(x^2-9)(x^2-4)`

`=(x^2-3^2)(x^2-2^2)`

`=(x-3)(x+3)(x-2)(x+2)`

Hence zeros:

`+-3`, `+-2`