Discriminant Calculator

The discriminant of a quadratic equation tells you, before you do any further work, exactly how many real solutions the equation has and what kind they are. For the quadratic ax squared plus bx plus c equals zero, the discriminant is Delta = b squared minus 4ac. This expression sits under the square root sign in the quadratic formula, and its sign determines everything about the roots. When Delta is greater than zero the square root is real and positive, so the formula gives two distinct real roots. When Delta equals zero the square root disappears, leaving one unique solution called a repeated or double root. When Delta is less than zero the square root of a negative number is not real, meaning the equation has no real solutions; the roots are complex conjugate numbers. You enter the three coefficients, a for the squared term, b for the linear term, and c for the constant, and the calculator returns the discriminant value, the root type classification, and the actual roots when they are real. The repeated-root case with Delta = 0 is particularly useful to recognise because it means the quadratic is a perfect square and the parabola just touches the x axis at exactly one point. This tool is useful for students studying quadratic equations and parabolas, for anyone who needs to quickly classify an equation before solving it, and for teachers setting exercises that require specific root types. The coefficients can be any signed decimal values as long as a is not zero.

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When the discriminant is negative the roots are complex and are not shown. Coefficients can be any signed decimals; a must not be zero.