The Quadratic Equation Solver solves equations in the form ax² + bx + c = 0. Enter the three coefficients to see the discriminant, equation, and real or complex roots.
Formula
The discriminant determines the root type: positive gives two real roots, zero gives one repeated real root, and negative gives a conjugate pair of complex roots. Coefficient a cannot be zero.
Example
For x² - 5x + 6 = 0, the discriminant is 25 - 24 = 1. The roots are (5 + 1) / 2 = 3 and (5 - 1) / 2 = 2.
Questions
What if the discriminant is negative?
The solver returns two roots with the same real part and opposite imaginary parts.
Can a be zero?
No. If a = 0, the equation is linear rather than quadratic and the calculator reports an error.
Are roots rounded?
The calculation returns JavaScript numeric values; display formatting is handled by the component.
Limitations
This solver handles numeric coefficients only. It does not simplify symbolic expressions, factor polynomials, or report exact radical notation.