Quadratic Real Roots
Solve ax² + bx + c = 0 with a nonzero leading coefficient. Receive both real roots or a clear error when no real roots exist.
How to use Quadratic Real Roots
- Enter “Coefficient a (nonzero)”, using the units and limits shown in its label.
- Enter “Coefficient b”, using the units and limits shown in its label.
- Enter “Coefficient c”, using the units and limits shown in its label.
- Select Calculate or Process. Review the result and any validation message before copying or downloading available output. Reset clears the result and restores the starting inputs.
Method & assumptions
Discriminant D = b² − 4ac; a cancellation-resistant quadratic calculation yields the two roots.
Worked example
x² − 3x + 2 = 0 has roots 1 and 2.
Results and projections are informational estimates, not financial, medical, legal, tax, or property advice. Check assumptions, units, rounding, and local requirements independently. Investment illustrations do not guarantee returns. Keep original files and check transformed output before use.
Questions, answered
Does this show imaginary roots?
No. Negative discriminants are reported as having no real roots. Use a linear solver if a is zero.
Where does this calculation run?
It runs locally in your browser. Enter plain numbers without currency symbols or thousands separators; use the same currency and measurement units throughout unless a converter explicitly asks for units.