Discriminant calculator
Enter a, b and c to find b² − 4ac and what it says about the roots, before solving anything.
For
Discriminant
Two distinct rational roots, so the quadratic factors over the integers.
Solve it with stepsReading the discriminant
| Value of D | Number and type of roots |
|---|---|
| D > 0, perfect square | 2 rational roots (factorable) |
| D > 0, not a perfect square | 2 irrational roots |
| D = 0 | 1 repeated rational root |
| D < 0 | 0 real roots, 2 complex roots |
The discriminant is the part of the quadratic formula under the square root, so it controls whether that root is real, zero or imaginary.
Frequently asked questions
What is the discriminant?
For ax² + bx + c, the discriminant is D = b² − 4ac, the expression under the square root in the quadratic formula.
What does a discriminant of 0 mean?
The quadratic has exactly one real root (a double root), x = −b/2a, and its parabola touches the x-axis at the vertex.
How do I know if a quadratic factors?
With integer coefficients, it factors over the integers exactly when the discriminant is a perfect square (0, 1, 4, 9, 16, …).