Quadratic formula calculator for roots and discriminant.
Enter coefficients for ax^2 + bx + c = 0 to find the discriminant and roots. This page is built for algebra practice, homework checking, and understanding what the quadratic formula is doing.
Find quadratic roots
Quadratic resultEnter a, b, and c to calculate roots.
Formula reference
Quadratic formula
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
- If the discriminant is positive, there are two real roots.
- If the discriminant is zero, there is one repeated real root.
- If the discriminant is negative, the roots are complex.
How to use this calculator
Put the equation into standard form first: ax^2 + bx + c = 0. Then enter the coefficients a, b, and c. For example, x^2 - 5x + 6 = 0 uses a = 1, b = -5, and c = 6.
Related learning
Use the Algebra Basics Calculator for linear equations, the Scientific Calculator for numeric checks, and the Essential Algebra Formulas guide for formula review.
FAQ
What does the discriminant tell me?
The discriminant, b^2 - 4ac, tells you how many real roots the quadratic has.
Can a be zero?
No. If a is zero, the equation is linear rather than quadratic. Use the algebra calculator for that case.