Quadratic Formula
The quadratic formula comes from completing the square on ax² + bx + c = 0. It produces both roots in one step.
Variables
- a — Coefficient of x² (cannot be 0)
- b — Coefficient of x
- c — Constant term
When to use it
Use it whenever a quadratic does not factor quickly, or to confirm factoring.
Worked example
x² − 5x + 6 = 0
- a=1, b=-5, c=6
- Δ=1
- x=3 or x=2
Answer: x = 2, x = 3
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Example problems
Common mistakes
Forgetting 2a in the denominator
The entire −b ± √Δ is divided by 2a, not only the square root.
Related formulas
Related calculators
Frequently asked questions
What is the discriminant?
b² − 4ac. Positive: two real roots. Zero: one real root. Negative: two complex roots.