What are all of the real roots of the following polynomial? f (x) = x4 - 13x2 + 36?

We can split the middle term to simplify this expression.

Doing so gives us (x^2 - 4) (x^2 - 9)

Using the difference of perfect squares rule, we can simplify this even further:

(x + 2) (x - 2) (x + 3) (x - 3)

The real roots of the polynomial are:

-2, 2, - 3, 3.