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.