Power Calculators

Δ Quadratic Discriminant Calculator

Calculate the discriminant of ax^2 + bx + c = 0 and identify the root type.

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Discriminant Δ
1

Also available in our Android app, with charts and full breakdown tables.

📘 About the Discriminant

The discriminant indicates whether a quadratic has two real roots, one repeated real root, or complex roots.

🧮 Formula

Where

  • a,b,c = coefficients in ax² + bx + c = 0
Δ = b² - 4ac.

✏️ Worked example

x² - 5x + 6 = 0

You enter
a1
b-5
c6
You get
Discriminant Δ1

The discriminant is 1.

Try this example →

🧭 How to use this calculator

What you enter

  • a
  • b
  • c

What you get

  • Discriminant Δ

💡 Interpretation

  • Δ > 0 gives two distinct real roots.
  • Δ = 0 gives one repeated real root.
  • Δ < 0 gives a complex conjugate pair.

❓ Frequently asked questions

What is the discriminant used for?

It helps classify the roots of a quadratic equation before calculating them.