Quadratic Formula Calculator
Discriminant, two real roots, a repeated root, or a complex pair. Click any i for detail.
Coefficients
a
i
a
Coefficient of x². If a is 0 this is linear, not quadratic. |
|
|---|---|
b
i
b
Coefficient of x. |
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c
i
c
Constant term. |
How to use this calculator
- Enter a, b, and c.
- Read the discriminant and roots.
- If a is 0 we fall back to a linear solve.
- Complex roots show as a ± bi.
Results explained
x = (−b ± √(b² − 4ac)) / (2a). Discriminant d = b² − 4ac. d > 0 two reals, d = 0 one real, d < 0 complex conjugates.
Quick reference: quadratics
x² − 5x + 6 = (x − 2)(x − 3).
| Item | Detail |
|---|---|
| d > 0 | Two real roots |
| d = 0 | Repeated real root |
| d < 0 | Complex pair |
| a = 0 | Linear bx + c = 0 |
This is algebra — not a graphing calculator.
How the estimate is built
x = (−b ± √(b² − 4ac)) / (2a).
Example scenario
a=1, b=−5, c=6 → d=1, roots 2 and 3.
FAQ
Vertex?
x = −b/(2a) is the axis of symmetry — not printed as a separate mode.
Fractions?
Enter decimals; we do not keep exact radicals.
Graphing?
Not on this page.