Math Doubts

Nature of Roots of a Quadratic equation

The discriminant of a quadratic equation determines the nature of the roots of the quadratic equation. The discriminant ($\Delta$ or $D$) is $b^2-4ac$ for the standard form quadratic equation $ax^2+bx+c = 0$.

There are six properties, which we need to understand to study the nature of roots of a quadratic equation. Learn all of them one after one with understandable examples.

Zero discriminant

The roots are real and equal if the discriminant of a quadratic equation is equal to zero.

Positive discriminant

The roots are two distinct real numbers if the discriminant is positive.

The roots are two distinct real and rational numbers if the discriminant is positive and can be expressed as a perfect square of another number, and the quadratic equation contains rational coefficients.

The roots are two distinct real and irrational numbers if the discriminant is positive and cannot be expressed as a perfect square of another number, and the quadratic equation contains rational coefficients.

Negative discriminant

The roots are different imaginary numbers and complex conjugates if the discriminant of a quadratic equation is less than zero.

04

Nonzero Discriminant

There are two distinct roots if the discriminant is not equal to zero.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved