The roots of a polynomial are also called its zeroes. These are the x-values when the function is equal to zero.
To determine how many roots a polynomial will have, examine the highest degree of the polynomial, that is, the term with the highest exponent.
That exponent is how many roots the polynomial will have. So if the highest exponent in your polynomial is 2, it'll have two roots; if the highest exponent is 3, it'll have three roots; and so on.