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Quadratic equation roots Calculator
Solve ax² + bx + c = 0 with real, repeated or complex roots and the discriminant. This free quadratic equation roots calculator shows the calculation and its assumptions so you can compare your own figures.
Your results
Solve ax² + bx + c = 0 with real, repeated or complex roots and the discriminant.
Calculated outcomes
- Discriminant
- 1
- Root Type
- Two real roots
Assumptions and estimates
- Floating-point coefficients. The stable q formula reduces cancellation in the roots; extremely close discriminants remain limited by floating-point precision.
- Method: Discriminant D = b² − 4ac. For real roots use stable q = −(b + sign(b)√D)/2, then q/a and c/q; for D < 0 return complex conjugates.
- a must be non-zero. Floating-point coefficients are bounded; near-zero discriminants remain subject to finite-precision limitations. This is not a symbolic algebra engine.
Useful next steps
- Use Compare options to test an alternative side by side.
- Copy, print or download a record of this calculation when you need one.
Reports open your email app addressed to s@s1.ie with the public page address only. Your inputs are never added.
How the quadratic equation roots calculation works
Discriminant D = b² − 4ac. For real roots use stable q = −(b + sign(b)√D)/2, then q/a and c/q; for D < 0 return complex conjugates.
a must be non-zero. Floating-point coefficients are bounded; near-zero discriminants remain subject to finite-precision limitations. This is not a symbolic algebra engine.
Using this calculator
- Enter your own figures in the labelled inputs. Keep the currencies, units and time periods consistent.
- Choose any applicable rate profile, pattern or assumption shown for this tool. Open additional inputs when relevant.
- Review root1 and root2, then read the stated assumptions and eligibility conditions before using the result.
Worked example
This is a static example using illustrative inputs, not facts about you or today’s date. The displayed eligibility selections and assumptions apply only to this example.
See example inputs
- Coefficient a (x²)
- 1
- Coefficient b (x)
- -5
- Constant c
- 6
- Root1
- 2
- Root2
- 3