Calculadora da Fórmula Quadrática (Bhaskara)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
x = (−b ± √Δ) / 2a ; Δ = b² − 4ac
About this calculator
The Quadratic Formula Calculator (Bhaskara) solves quadratic equations in the standard form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It uses the Bhaskara formula to find the real roots, first calculating the discriminant Δ = b² − 4ac. If Δ is greater than or equal to zero, the roots are real and computed as x = (−b ± √Δ) / 2a. If Δ is negative, the calculator indicates no real roots, as the square root of a negative number is not real.
How it works: you enter the coefficients a, b, and c. The calculator checks that a is nonzero, computes Δ, and if Δ ≥ 0, applies the formula. The result shows the two roots, when they exist. For example, for the equation x² − 5x + 6 = 0 (a=1, b=-5, c=6), Δ = 1, and the roots are x = 2 and x = 3. The tool is useful for students, teachers, and professionals who need to quickly solve quadratic equations without manual calculation errors.
When to use: in physics problems (uniformly accelerated motion), engineering (equilibrium points), economics (cost analysis), financial mathematics (compound interest), and any context involving quadratic equations. It is also handy for checking answers to exercises or simulations.
Cautions: make sure coefficient a is not zero, otherwise the equation is not quadratic. Remember that the formula only yields real roots; for complex roots, you need complex numbers. Also, double-check the input of coefficients, especially negative signs, to avoid calculation errors.
Frequently asked questions
What does it mean if the discriminant Δ is negative?
When Δ < 0, the equation has no real roots, because the square root of a negative number is not a real number. In this case, the roots are complex (imaginary numbers).
Can I use the calculator if a is zero?
No. If a = 0, the equation is not quadratic, and the quadratic formula does not apply. The calculator will require a to be nonzero.
How many roots can a quadratic equation have?
It depends on the discriminant: if Δ > 0, two distinct real roots; if Δ = 0, one real double root; if Δ < 0, no real roots (two complex roots).
Does the calculator show exact or decimal roots?
It displays roots in approximate decimal form. For exact values, you can use the radical expression, but the calculator simplifies to a numeric value.
How do I know if I entered the coefficients correctly?
Check the signs: for example, for the equation 2x² - 3x + 1 = 0, the coefficients are a=2, b=-3, c=1. If the result seems off, double-check your input.