Question

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

Answer 1

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.