Resuelve ecuaciones cuadráticas ax² + bx + c = 0 al instante. Obtén raíces reales y complejas, discriminante, vértice y solución paso a paso. Gratis y 100% del lado del cliente.
This quadratic equation solver instantly finds the roots of any equation in the form ax² + bx + c = 0. It calculates the discriminant, determines the nature of the roots (real or complex), finds the vertex and axis of symmetry, and shows a complete step-by-step solution. Perfect for students, teachers, and engineers. All calculations happen in your browser — no data is sent to any server.
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It gives the solution(s) to any quadratic equation of the form ax² + bx + c = 0, where a ≠ 0.
The discriminant is D = b² − 4ac. It tells you the nature of the roots: if D > 0, two distinct real roots; if D = 0, one repeated real root; if D < 0, two complex conjugate roots.
The vertex is the turning point of the parabola. For a quadratic equation, the vertex coordinates are (−b/2a, −D/4a), where D is the discriminant. If a > 0, the parabola opens upward and the vertex is a minimum; if a < 0, it opens downward and the vertex is a maximum.
Yes. When the discriminant is negative, the solver displays the roots as complex numbers in the form x = p ± qi, where p and q are real numbers and i is the imaginary unit (√−1).