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 x2 – 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.
x2 – 9 = 0
x2 = 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 x2 – 9.