Quadratic Formula Calculator
Solve ax² + bx + c = 0
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The Quadratic Formula
The Discriminant
Example
Solve x² − 5x + 6 = 0 (a=1, b=−5, c=6):
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula solves any equation in the form ax² + bx + c = 0. The solution is x = (−b ± √(b²−4ac)) / 2a. The ± symbol means there are two possible solutions (x₁ and x₂), which may be equal if the discriminant is zero.
What is the discriminant?
The discriminant is b² − 4ac. If positive, the equation has two distinct real roots. If zero, it has exactly one real root (a repeated root). If negative, it has two complex (imaginary) roots — the parabola does not cross the x-axis.
Can I use the quadratic formula if a = 0?
No. If a = 0, the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula divides by 2a and requires a ≠ 0. Solve linear equations as x = −c/b.
What does it mean to have complex roots?
Complex roots occur when the discriminant is negative. They come in conjugate pairs: x = p ± qi where i = √−1. Complex roots mean the parabola y = ax² + bx + c never intersects the x-axis.