Quadratic equation solver
Enter the coefficients of ax2 + bx + c = 0 to find its roots, discriminant, vertex, and factored form. Roots may be real or complex.
How it works
The roots come from the quadratic formula, x = (−b ± √(b2 − 4ac)) / 2a. The quantity under the root, Δ = b2 − 4ac, is the discriminant and decides the nature of the roots:
Δ > 0 → two distinct real roots · Δ = 0 → one repeated real root · Δ < 0 → two complex-conjugate roots.
The parabola's vertex sits at x = −b / 2a, which is also the axis of symmetry. By Vieta's formulas the roots sum to −b/a and multiply to c/a. When the roots are rational, a factored form is shown. If a = 0 the equation is linear, and its single root is reported.