About this calculator
When the discriminant is negative, the roots are complex and shown with i.
How to use it
- Enter a, b and c.
- Read the roots and other details.
The formula
x = (−b ± √(b² − 4ac)) ÷ 2a
- b² − 4ac
- discriminant
- vertex
- (−b ÷ 2a, c − b² ÷ 4a)
Worked example
x² − 5x + 6 = 0
- Discriminant = 25 − 24 = 1.
- x = (5 ± 1) ÷ 2, so x = 3 or x = 2.
- Vertex at (2.5, −0.25).
What the result means
Sum of roots = −b/a and product = c/a, a quick check.
Assumptions
- All lengths in the same unit.
Limitations
- Results are rounded to 10 significant figures.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a.
What if the discriminant is negative?
The roots are complex: real part −b/2a and imaginary part √(−D)/2a.
Can a be zero?
No; then it is a linear equation.
Last reviewed on 3 October 2026. Found a mistake? Tell us.