Quadratic Equation Solver
Solve ax² + bx + c = 0. Returns both roots (real or complex), the discriminant, and the vertex of the parabola.
Solve ax² + bx + c = 0
Details
How to use
- 1
Enter the three coefficients a, b, c from ax² + bx + c = 0.
- 2
The solver returns both roots, the discriminant (which tells you the nature of the roots), and the vertex of the parabola.
- 3
If a = 0 the equation is linear — not solvable as quadratic. Use a different approach.
Frequently asked questions
The discriminant b² − 4ac determines the number and type of roots. Positive → two distinct real roots. Zero → one repeated real root (the parabola just touches the x-axis). Negative → two complex conjugate roots (the parabola doesn't cross the x-axis).
The vertex is the highest or lowest point of the parabola y = ax² + bx + c. Its x-coordinate is −b / (2a) — the axis of symmetry. The y-coordinate is the value of the function at that x. If a > 0 the vertex is a minimum; if a < 0 it's a maximum.
Complex roots take the form p ± qi, where p is the real part and qi is the imaginary part. For ax² + bx + c = 0 with negative discriminant: p = −b / (2a), q = √(4ac − b²) / (2a). The calculator displays both parts separately.
If a = 0, the x² term vanishes and the equation becomes bx + c = 0 — a linear equation with at most one solution. The quadratic formula divides by 2a, so a = 0 makes the formula undefined.
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Source: Standard quadratic formula · Last verified 2026-06. This tool provides estimates only and is not legal, tax or financial advice. Always verify your specific situation with the relevant UAE authority or a licensed advisor before taking action.