Quadratic Equation Solver
Solve ax² + bx + c = 0, where a is the x² coefficient, b the x coefficient and c the constant. A dash means there are no real roots. Enter…
8 of 8 free uses remaining today
Solve ax² + bx + c = 0, where a is the x² coefficient, b the x coefficient and c the constant. A dash means there are no real roots. Enter coefficient a, coefficient b and constant c to see discriminant, root 1 and root 2 when you calculate.
Worked example
Example calculated from the starting values. Enter your own values and press Calculate to get your result.
With the default inputs (coefficient a = 1, coefficient b = -3, constant c = 2), the results are: discriminant 1.000; root 1 2.0000; root 2 1.0000.
Quick reference: coefficient a vs result
Reference table based on the example values; it is not your calculation result.
| Coefficient a | Discriminant | Root 1 | Root 2 |
|---|---|---|---|
| 0.5 | 5.000 | 5.2361 | 0.7639 |
| 1 | 1.000 | 2.0000 | 1.0000 |
| 2 | -7.000 | — | — |
| 5 | -31.000 | — | — |
| 10 | -71.000 | — | — |
| 20 | -151.000 | — | — |
Frequently asked questions
What formula does this calculator use?
Discriminant = b^2-4 × a × c; Root 1 = (-b+sqrt(b^2-4 × a × c)) ÷ (2 × a); Root 2 = (-b-sqrt(b^2-4 × a × c)) ÷ (2 × a). Variables: a = coefficient a, b = coefficient b, c = constant c.
What do I need to enter?
You need coefficient a, coefficient b, constant c. Results update as you type.
What is an example result?
With the default inputs (coefficient a = 1, coefficient b = -3, constant c = 2), the results are: discriminant 1.000; root 1 2.0000; root 2 1.0000.
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