Discriminant

The discriminant of a quadratic function in the form

$ax^{2} + bx + c = 0$

is equal to

$D = b^2 - 4ac$

Since the square root of the discriminant is used in the quadratic formula in the form

$\displaystyle x = \frac{-b \pm \sqrt{D}}{2a}$

it can be used to determine how many roots the function has. If it is greater than zero, the function has two real roots, if it is equal to zero, the function has one, and if it is negative, the function will only have imaginary roots.