Math & Conversions

Discriminant Calculator

Find the discriminant of a quadratic ax^2 + bx + c by computing b^2 - 4ac, and see whether the equation has two real, one repeated, or two complex roots.

What this calculator does

The Discriminant Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Find the discriminant of a quadratic ax^2 + bx + c by computing b^2 - 4ac, and see whether the equation has two real, one repeated, or two complex roots. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Discriminant Calculator

Result

—
Discriminant
—
Nature of Roots

About Discriminant Calculator

For a quadratic written as ax² + bx + c = 0, the discriminant is b² − 4ac. Enter the three coefficients and this tool returns that value plus a plain-language reading of what it means for the roots.

A positive discriminant means two distinct real roots, zero means one repeated real root, and a negative value means two complex conjugate roots.

Formula & Mathematical Calculation

Discriminant = f(a, b, c)

Calculated according to standard math formulas implemented in the calculator core.

Calculation Example

Enter a = 1, b = -3, and c = 2, then press Calculate. The tool computes (−3)² − 4×1×2 = 9 − 8 = 1. It shows Discriminant = 1 and Nature of Roots = Two distinct real roots, with the note "b^2 - 4ac = 1: Two distinct real roots."

Key Benefits

  • Calculates b^2 - 4ac from your a, b, and c without hand arithmetic.
  • Classifies the roots as two real, one repeated, or two complex based on the sign of the result.
  • Free, runs in the browser, and requires no account.

How to Use this Calculator

  1. Enter coefficient a
    Type the coefficient of x squared into the a field.
  2. Enter b and c
    Fill in the b field with the x coefficient and the c field with the constant term.
  3. Calculate
    Press Calculate to see the Discriminant value and the Nature of Roots description.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Discriminant Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

It reads the sign of the discriminant: positive gives two distinct real roots, zero gives one repeated real root, and negative gives two complex roots.

Field a is the coefficient of x squared, b is the coefficient of x, and c is the constant term.

b squared is 9 and 4ac is 8, so 9 minus 8 equals 1, indicating two distinct real roots.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.