Quadratic roots, real or complex
Enter a, b and c for ax² + bx + c = 0 and get both roots, the discriminant, the vertex and the factored form — real, repeated or complex roots are all handled, and a = 0 is solved as the linear equation it actually is rather than rejected.
How to use
- Enter a, b and c
- Press Solve for the roots, discriminant and vertex
- Check the working panel for the full quadratic-formula derivation
Common questions
What happens if I set a = 0? Is that still a quadratic?
No — with a = 0 the x² term disappears and the tool solves it as the straight line it actually is (bx + c = 0), rather than refusing the input or dividing by zero.
Does it handle equations with no real roots?
Yes — when the discriminant is negative, it returns the two complex conjugate roots in the form a ± bi rather than showing an error.
What does the "factored form" row actually show?
The equation rewritten as a(x − r₁)(x − r₂) using the roots it just found, with a repeated root shown as a squared bracket. It's only shown for real roots, since factoring over complex roots isn't what this row is for.