Quadratic Equation Solver
Solve quadratic equations (ax² + bx + c = 0) and display real and complex roots with step-by-step working. Free, browser-based.
🧮 Math & Finance Tools
Free
Browser-based
1x² + 0x + 0 = 0
a (x² coefficient)
Must not be 0
b (x coefficient)
c (constant)
The Quadratic Formula
Every quadratic equation ax² + bx + c = 0 (where a ≠ 0) can be solved using:
x = (−b ± √(b² − 4ac)) / 2a
The Discriminant (Δ = b² − 4ac)
| Discriminant | Root Type | Graph |
|---|---|---|
| Δ > 0 | Two distinct real roots | Parabola crosses x-axis twice |
| Δ = 0 | One repeated real root | Parabola touches x-axis once |
| Δ < 0 | Two complex conjugate roots | Parabola does not cross x-axis |
Key Properties
Vertex: (−b/2a, c − b²/4a) — the turning point of the parabola.
Axis of symmetry: x = −b/2a — vertical line through the vertex.
y-intercept: (0, c) — where the parabola crosses the y-axis.