Discriminant Calculator

Work out discriminant instantly with clear inputs, formula shown and shareable results.

About Discriminant Calculator

The discriminant Δ = b² − 4ac sits under the square root in the quadratic formula, so its sign decides everything: positive gives two real roots, zero a repeated root, negative a complex conjugate pair.

Formula

Discriminant

Δ = b² − 4ac

Worked example

With the default values below, Discriminant Calculator returns Discriminant b² − 4ac of 25.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a: 2
Coefficient b: -7
Coefficient c: 3

Results

Discriminant b² − 4ac: 25.00000000
Nature of the roots: Two distinct real roots
√Δ (0 when negative): 5.00000000
Rational roots: Yes, the roots are rational

Step by step

1Values used
2Discriminant
3Discriminant b² − 4ac= 25.00000000
4Nature of the roots= Two distinct real roots
5√Δ (0 when negative)= 5.00000000
6Rational roots= Yes, the roots are rational

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 2x² − 7x + 3?

Δ = 49 − 24 = 25, a perfect square, so the roots 3 and 0.5 are rational.

What if Δ is positive but not a perfect square?

The roots are real but irrational, involving a surd such as √13.