Quadratic Equation Solver
This solver finds the roots of using the quadratic formula, and shows the actual computed steps — discriminant, square root, and both branches. It handles two real roots, a repeated root, and complex conjugate roots.
Inputs
Frequently asked questions
What does the discriminant tell me?
The discriminant Δ = b² − 4ac decides the nature of the roots without solving: Δ > 0 gives two distinct real roots, Δ = 0 gives one repeated real root, and Δ < 0 gives a pair of complex conjugate roots.
Can this solver handle complex roots?
Yes. When Δ < 0 the solver takes √(−Δ) and writes the answer as a ± bi, showing the real and imaginary parts as separate computed steps.
Why must a be non-zero?
If a = 0 the x² term vanishes and the equation becomes linear (bx + c = 0), which has a single root x = −c/b. The quadratic formula divides by 2a, so it is undefined at a = 0.