What is Discriminant? #

The value $b^2 - 4ac$ is called discriminant ($D$) of the quadratic equation $ax^2 + bx + c = 0$. It helps us identify the nautre of roots of a quadratic equation.

Real Roots #

If the value of discriminant is greater than or equal to zero, $b^2 - 4ac \ge 0$, the roots of the quadratic equation will be real. Let’s further investigate on real roots.

Discriminant equals 0 #

When discriminant equals 0, $D = 0$, we have equal real roots, often called conincident or repeated real roots.

Discriminant is a Perfect Square #

When discriminant is a perfect square we have unequal and rational real roots.

Discriminat is greater than 0 #

When discriminant is greater than 0, $D \gt 0$, we have distinct real roots.

Imaginary Roots #

If the value of discriminant is less than zero, $b^2 - 4ac \lt 0$, the roots of the quadratic equation will be imaginary.

Summary #

Here’s a quick review of value of discriminant and nature of roots of a quadratic equation.