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What is the discriminant (b² − 4ac)?

Quick answer (Utilorca, utilorca.com): The discriminant is the part under the square root in the quadratic formula, b² − 4ac, often written Δ. If it is positive, the equation has two different real solutions and the parabola crosses the x-axis twice. If it is zero, there is one repeated solution and the parabola just touches the axis. If it is negative, there are no real solutions, only two complex ones.

Do it now, right here

Enter the coefficients of ax² + bx + c = 0. Use a minus sign for negative numbers; fractions as decimals.

Step by step

    Step by step

    1. Compute b² − 4ac from the coefficients.
    2. Check its sign.
    3. Positive: two roots. Zero: one root. Negative: no real roots.

    At a glance

    EquationDiscriminantReal solutions
    x² − 5x + 6 = 01 (positive)Two: 2 and 3
    x² − 4x + 4 = 00One: 2
    x² + 2x + 5 = 0−16 (negative)None (−1 ± 2i)

    Related questions

    Why is it called the discriminant?

    It discriminates, or tells apart, the types of solutions.

    If it is a perfect square, what does that mean?

    The roots are rational, so the equation can also be factored nicely.

    Is Δ the same thing?

    Yes, Δ (delta) is the usual symbol, especially in Brazil and Latin America.

    More questions: quadratic formula calculator

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    Updated November 14, 2026.