Discriminant Calculator

Discriminant Calculator

Calculate the discriminant of a quadratic equation and identify the nature of its roots.

Last updated: June 2026 | By Patchworkr Team

Discriminant Solver

Coefficient a cannot be blank.

Discriminant
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Enter coefficients or load the example
Working will appear here after valid input is entered.

What is the Discriminant?

For the quadratic equation ax^2 + bx + c = 0, the discriminant is D = b^2 - 4ac.

How to Use This Calculator

  1. Enter the coefficients a, b, and c from ax^2 + bx + c = 0.
  2. Make sure a is not zero because the equation must be quadratic.
  3. Read the discriminant and the type of roots on the right.

Worked Example

For x^2 + 5x + 6 = 0, D = 5^2 - 4(1)(6) = 1.

Since D > 0, the equation has two distinct real roots.

Frequently Asked Questions

What if D is positive?

A positive discriminant means the quadratic has two distinct real roots.

What if D is zero?

A zero discriminant means the quadratic has one repeated real root.

What if D is negative?

A negative discriminant means the quadratic has two complex roots.

Does a have to be nonzero?

Yes. If a is zero, the equation is not quadratic and the discriminant is not meaningful here.

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