Solve any quadratic equation ax² + bx + c = 0 instantly. Find real and complex roots, vertex, axis of symmetry, discriminant, and see the parabola plotted on a live chart.
x = (−b ± √(b² − 4ac)) ÷ 2a
Discriminant Δ = b² − 4ac: Δ > 0 → two distinct real roots; Δ = 0 → one repeated root; Δ < 0 → two complex roots.
Example: x² − 5x + 6 = 0. a=1, b=−5, c=6. Δ = 25−24 = 1. x = (5 ± 1) ÷ 2. Roots: x₁ = 3, x₂ = 2.
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It gives the roots (solutions) of any equation in the form ax² + bx + c = 0.
The discriminant (b² − 4ac) tells you the nature of the roots. Positive = 2 real roots; zero = 1 repeated root; negative = 2 complex (imaginary) roots.
The vertex is the highest or lowest point of the parabola, located at x = −b/2a, y = c − b²/4a.
Yes — when the discriminant is negative (b² − 4ac < 0), the roots are complex numbers involving the imaginary unit i.
The axis of symmetry is the vertical line x = −b / (2a), which passes through the vertex of the parabola.