Discriminant Calculator
Enter the coefficients a, b, and c of a quadratic equation to compute its discriminant and learn the number and type of roots.
Two distinct real roots
- 1
b² (b squared)
5 × 5 = 25 - 2
4ac
4 × 1 × 6 = 24 - 3
Discriminant D = b² − 4ac
25 − 24 = 1
How does this calculator work?
The discriminant D = b² − 4ac of a quadratic ax² + bx + c = 0 tells you the nature of its roots. If D is positive there are two distinct real roots, if D equals zero there is one repeated real root, and if D is negative there are two complex conjugate roots.
Formula
How this is calculated
A quadratic equation has the form ax² + bx + c = 0, where a, b, and c are the coefficients you enter. The coefficient a must be non-zero, otherwise the equation is linear rather than quadratic and the discriminant is undefined.
The discriminant is D = b² − 4ac. It is the expression under the square root in the quadratic formula, so its sign determines the nature of the roots without solving the equation. When D > 0 there are two distinct real roots; when D = 0 there is exactly one repeated (double) real root; when D < 0 there are no real roots, only a pair of complex conjugate roots.
All inputs are unitless coefficients and the discriminant is likewise unitless. The segmented scale highlights whether D lands in the negative, zero, or positive region. Note that exact equality D = 0 depends on the precision of your inputs, so values extremely close to zero from rounding may be reported as positive or negative.
Frequently asked questions
Its sign reveals the nature of a quadratic’s roots: positive means two distinct real roots, zero means one repeated real root, and negative means two complex conjugate roots.
If a = 0 the term ax² disappears and the equation becomes linear (bx + c = 0), so the discriminant b² − 4ac no longer describes a quadratic and is not defined here.
Yes. The discriminant is commonly written as the Greek letter delta (Δ), and both refer to the quantity b² − 4ac.
Also known as
TG we-Calculate Editorial Team. (2026). Discriminant Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/discriminant-calculator
TG we-Calculate Editorial Team. "Discriminant Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/discriminant-calculator.
TG we-Calculate Editorial Team, "Discriminant Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/discriminant-calculator
@misc{wecalculate_discriminant_calculator, title = {Discriminant Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/discriminant-calculator}}, year = {2026}, note = {TG we-Calculate} }
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