Quadratic Formula Calculator
Solve ax² + bx + c = 0 for x using the quadratic formula, including complex roots.
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- Accurate results
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- Works on all devices
Enter the coefficients a, b, and c to solve a quadratic equation for x.
Your result
2
Root 1
Root 21
Discriminant1
Nature of rootsTwo distinct real roots
AI explanation
Formula
x = (−b ± √(b² − 4ac)) ÷ 2aWorked example
x² − 3x + 2 = 0
| Field | Value |
|---|---|
| Coefficient a | 1 |
| Coefficient b | -3 |
| Coefficient c | 2 |
| Root 1 | 2 |
| Root 2 | 1 |
| Discriminant | 1 |
| Nature of roots | Two distinct real roots |
Assumptions
- When the discriminant (b² − 4ac) is negative, the roots are complex — reported as text rather than left undefined.
Frequently asked questions
What is the discriminant?
b² − 4ac — its sign tells you the nature of the roots: positive means two real roots, zero means one repeated real root, and negative means two complex conjugate roots.
What if a = 0?
Then the equation isn't actually quadratic — use the Linear Equation Calculator instead for ax + b = 0.
How are complex roots shown?
As text in the form "real ± imaginary i" — for example, "-0.5 + 0.87i".