How quadratic equation solver works
A quadratic equation has the form ax² + bx + c = 0, where a is not zero. Its solutions come from the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The expression under the square root, b² − 4ac, is called the discriminant and it tells you the nature of the roots before you solve.
If the discriminant is positive the equation has two distinct real roots. If it is zero the two roots coincide into one repeated real root. If it is negative the roots are complex conjugates, written as p ± qi where i is the imaginary unit. This solver reports the discriminant, classifies the roots, and lists them in exact rounded form.
Enter the coefficients a, b, and c. The calculator applies the quadratic formula and returns the roots and the discriminant. It rejects a = 0 because that would make the equation linear rather than quadratic. Use it for algebra homework, physics problems, and any model involving a squared term.