All equation has always
even numbers of imaginary roots because they always come in pairs. Therefore
there must be either 2 imaginary roots, or zero.
To determine the types of roots, we could try synthetic
division by some of the factors of the number -32. The simplest factors are +1
or -1. Using this, we can quickly show that (x + 1) is a factor, and leaving
(x² + 4x - 32) as the remainder. This remainder equation then factorises to (x
- 4) (x + 8).
So to conclude there are three real zeros which are:
x = -1
x = 4
x = -8
