Quadratic Formula Solver
Solve ax² + bx + c = 0 using the quadratic formula. Get real and complex roots with full step-by-step working and discriminant analysis.
x = (−b ± √(b²−4ac)) / 2a
Step-by-step solution
The Quadratic Formula
For ax² + bx + c = 0, the solutions are x = (−b ± √(b²−4ac)) / 2a. The discriminant Δ = b²−4ac determines the nature of the roots: Δ>0 means two distinct real roots; Δ=0 one repeated root; Δ<0 two complex (imaginary) roots.
Frequently Asked Questions
What is the quadratic formula?
x = (−b ± √(b²−4ac)) / (2a). It solves any equation of the form ax² + bx + c = 0. The ± gives two solutions.
How do you solve x² − 5x + 6 = 0?
With a=1, b=−5, c=6: discriminant = 25 − 24 = 1. So x = (5 ± 1) / 2, giving x = 3 or x = 2.
When does a quadratic have no real solutions?
When the discriminant (b²−4ac) is negative. The equation then has two complex (imaginary) roots.