How do I know how many roots a quadratic equation has?

Let ax² + bx + c = 0 be the equation in question where a,b,c are real numbers with a not equal to 0 (otherwise we would not have a quadratic).

 

If:

b² - 4ac > 0 then there are two (real) roots

b² - 4ac = 0 then there is exactly one (real) root

b² - 4ac < 0 then there are no (real) roots.