About this calculator
Enter a, b and c of ax² + bx + c = 0.
How to use it
- Enter a, b and c.
- Read the discriminant and nature of roots.
The formula
D = b² − 4ac
- D > 0
- two distinct real roots
- D = 0
- two equal real roots
- D < 0
- no real roots
Worked example
2x² + 4x + 5 = 0
- D = 16 − 40 = −24.
- D is negative, so there are no real roots.
What the result means
If D is a perfect square and a, b, c are whole numbers, the roots are rational.
Assumptions
- All lengths in the same unit.
Limitations
- Results are rounded to 10 significant figures.
Frequently asked questions
What does a negative discriminant mean?
The roots are complex, not real.
When are roots equal?
When D = 0.
How do I find k for equal roots?
Set b² − 4ac = 0 and solve for k.
Last reviewed on 3 October 2026. Found a mistake? Tell us.