EVERYDAY MATH · FREE INTERACTIVE CALCULATOR
Quadratic Equation Solver
Find real or complex roots of ax² + bx + c = 0. Change the inputs below to calculate a result immediately. No account required.
Discriminant
1Root 1
2Root 2
1How to calculate the answer
Discriminant Δ = b² − 4ac. Roots are (−b ± √Δ)/(2a).
Worked example
x² − 3x + 2 = 0 has roots 1 and 2.
For the example inputs shown above, the calculated results are:
| Discriminant | 1 |
|---|---|
| Root 1 | 2 |
| Root 2 | 1 |
How to interpret this result
If a is zero, the equation is linear rather than quadratic.
These figures illustrate the displayed method using the default inputs. Change the inputs to explore another case, and check units and conventions relevant to the problem.
How many solutions are possible
The discriminant b² − 4ac determines whether a real quadratic has two distinct real roots, one repeated real root, or no real roots.
Check the coefficient
The coefficient of x² must be nonzero for an equation to be quadratic. Substitute computed roots back into the original expression as a cross-check.
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Frequently asked questions
How are quadratic roots found?
With the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a.
What is the discriminant?
b² − 4ac. If positive there are two real roots, if zero one, if negative two complex.
Can a be zero?
No. Then the equation is linear.
Sources and further reading
Last updated: . Results are estimates for information only and are not financial, medical or professional advice.