The roots of the quadratic function *f* (*x*) = *ax*^{2} + *bx** +*c are given by,

The number of roots is determined as follows:

1. *b*^{2} −4*ac*< 0 There are no real roots.

2. *b*^{2} −4*ac* = 0 There is one real root.

3. *b*^{2} −4*ac*> 0 There are two real roots.