Nature of roots of a quadratic equation

What is Discriminant? #

The value b24ac b^2 - 4ac is called discriminant (D D ) of the quadratic equation ax2+bx+c=0 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, b24ac0 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 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>0 D \gt 0 , we have distinct real roots.

Imaginary Roots #

If the value of discriminant is less than zero, b24ac<0 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.

Discriminant and Nature of Roots