Enter quadratic coefficients
Use the grid below. It becomes three, two, then one column.
Example data table
| Example | a | b | c | Discriminant | Root summary |
|---|---|---|---|---|---|
| x² - 5x + 6 = 0 | 1 | -5 | 6 | 1 | 2 and 3 |
| x² + 4x + 4 = 0 | 1 | 4 | 4 | 0 | -2 repeated |
| 2x² - 7x + 3 = 0 | 2 | -7 | 3 | 25 | 0.5 and 3 |
| x² + 2x + 5 = 0 | 1 | 2 | 5 | -16 | -1 ± 2i |
| 3x² + x - 2 = 0 | 3 | 1 | -2 | 25 | -1 and 0.6667 |
Formula used
The calculator first checks the discriminant. Positive values give two real roots. Zero gives one repeated root. Negative values produce complex conjugate roots.
How to use this calculator
- Enter values for a, b, and c.
- Keep a nonzero. Otherwise it is not quadratic.
- Choose the number of decimal places you want.
- Optionally set a custom x-range for the graph.
- Press Calculate roots to generate the result block.
- Review roots, discriminant, vertex, and intercept information.
- Use the CSV or PDF button to save results.
FAQs
1. What does this calculator solve?
It solves equations in the form ax² + bx + c = 0. It also reports the discriminant, vertex, intercepts, factorized form, and graph behavior.
2. Why must coefficient a stay nonzero?
If a equals zero, the x² term disappears. The equation becomes linear, so the quadratic formula and parabola graph no longer apply.
3. What does the discriminant tell me?
The discriminant shows the root type. Positive means two real roots. Zero means one repeated real root. Negative means two complex conjugate roots.
4. Can this page show complex roots?
Yes. When the discriminant is negative, the calculator reports roots using a real part and an imaginary part, written with i.
5. What is a repeated root?
A repeated root happens when the discriminant equals zero. The parabola touches the x-axis once, and both root values are identical.
6. How is the graph range selected?
If you leave graph limits blank, the chart centers around the axis of symmetry and expands enough to show the curve clearly.
7. Can I enter decimal coefficients?
Yes. The inputs accept integers and decimals, so you can explore scaled models, fitted curves, and non-integer algebra examples.
8. Why would I download CSV or PDF?
CSV is useful for spreadsheets and datasets. PDF is better for printing, sharing, archiving, or attaching a clean visual summary.