Discriminant

The discriminant of a Quadratic Equation of the form $a{x}^2+b{x}+{c}=0$ is the quantity $b^2-4ac$ . When ${a},{b},{c}$ are real, this is a notable quantity, because if the discriminant is positive, the equation has two real roots; if the discriminant is negative, the equation has two nonreal roots; and if the discriminant is 0, the equation has a real double root.