How to use the quadratic formula
Enter the three coefficients a, b, and c from your equation in the form ax² + bx + c = 0. The calculator applies the quadratic formula x = (−b ± √(b² − 4ac)) / (2a) and shows all roots. If the discriminant (b² − 4ac) is positive, there are two real roots. If it equals zero, there is one repeated root. If it is negative, the roots are complex conjugates.
Quadratic formula reference
x = (−b ± √(b² − 4ac)) / (2a). Discriminant D = b² − 4ac: D > 0 → two real roots; D = 0 → one real root (repeated); D < 0 → two complex roots. The sum of the roots equals −b/a and the product equals c/a (Vieta's formulas).
FAQ
What if a is zero?
If a = 0 the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula does not apply — the solution is simply x = −c/b.
What are complex roots?
When the discriminant is negative, there are no real solutions. The roots are complex numbers of the form p ± qi, where i is the imaginary unit (√−1). They always appear as conjugate pairs.