Lesson 3: The nature of the roots

From previous discussions, we know that an equation of the form has two roots, but the roots are not always distinct. Take, for example, the equation

We can see that x = –2 when y = 0. This occurs twice, so we call it a double root. It is a single distinct result, but still considered as two roots.

What happens when the equation will not factor over the set of real numbers? Consider

(1)

From equation (1) it is clear that when