# Roots of a Polynomial

The **roots** of a polynomial are the values of *x* (or whatever variable shows up in the polynomial) that make the entire polynomial have a value of zero when we evaluate the polynomial at those values. Think of it this way: there are two "0"s in the word "root." Fine, they're actually "o"s, but we won't tell anybody if you don't.

### Sample Problem

What are the roots of the polynomial *x*^{2} – 9?

We're looking for the *x*-values that turn the whole polynomial into a big, fat zero, so let's set it equal to zero and solve for *x*.

*x*^{2} – 9 = 0*x*^{2} = 9*x* = ±3

In other words, we can plug in either *x* = 3 or *x* = -3 to make our polynomial have a value of zero. This means 3 and -3 are the roots of the polynomial *x*^{2} – 9.

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