Calculadora de Discriminante
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Δ = b² − 4ac
About this calculator
The Discriminant Calculator is an online tool that calculates Δ (delta) of a quadratic equation in the form ax² + bx + c = 0. The discriminant is given by the formula Δ = b² − 4ac. Based on the result, it tells how many real roots the equation has: two distinct real roots if Δ > 0, one double real root if Δ = 0, or no real roots if Δ < 0. Simply input the coefficients a, b, and c to get the discriminant and classification.
It works simply: you enter the values of a, b, and c in the corresponding fields and click calculate. The tool applies the formula b² − 4ac and displays the value of Δ. Then it shows whether the equation has two different real solutions, one real solution (double root), or no real solution. This helps understand the nature of solutions without solving the entire equation.
Use this calculator when studying quadratic equations, solving high school math problems, or needing to quickly check the number of real roots of an equation. It is useful for students, teachers, and professionals dealing with quadratic functions. It can also be used in preliminary analysis before applying the quadratic formula.
Caution: ensure that coefficient a is not zero, otherwise the equation is not quadratic. Enter values correctly, including negative signs. Remember that the discriminant does not provide the roots themselves, only indicates the number of real roots. To find the roots, use the full quadratic formula.
Frequently asked questions
What does a negative discriminant mean?
It means the quadratic equation has no real roots; the parabola does not intersect the x-axis. The roots are complex numbers.
Can I use this calculator if a is zero?
No, if a = 0 the equation is not quadratic, and calculating the discriminant is meaningless. The calculator may return an error or invalid result.
Does the discriminant give me the roots of the equation?
No, the discriminant only indicates how many real roots exist. To find the roots, use the quadratic formula: x = (-b ± √Δ) / (2a).
What is the difference between discriminant and delta?
They are the same thing. Discriminant is the technical name, and delta (Δ) is the Greek letter used to represent it.
What happens if the discriminant is zero?
The equation has a single real root (double root); the parabola touches the x-axis at one point.