How to use the Quadratic Formula Calculator
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The formula
x = (−b ± √(b² − 4ac)) ÷ 2a
Examples
- x² − 3x + 2 = 0
Discriminant: 1 Two real roots: x₁ = 2 x₂ = 1
- x² + 2x + 1 = 0 (one repeated root)
Discriminant: 0 One repeated real root: x = -1 Vertex: (-1, 0)
- x² + x + 1 = 0 (complex roots)
Discriminant: -3 Two complex roots: x = -0.5 ± 0.8660254i Vertex: (-0.5, 0.75)
Limitations and assumptions
Computed in your browser with standard double-precision arithmetic unless the page says otherwise. Very large or very small values may be rounded.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a.
What does the discriminant tell me?
b² − 4ac positive means two real roots, zero means one repeated root, negative means two complex roots.
What if a is zero?
The equation is linear, not quadratic, so use x = −c ÷ b.
How can I check the answer?
Substitute each root back into the equation; it should equal zero.