Your result
How this calculation works
Discriminant D = b² − 4ac. Roots = (−b ± √D) ÷ 2a. A stable equivalent is used for real roots to reduce subtraction error.
Enter three coefficients with a nonzero quadratic coefficient. Results include the discriminant and both real or complex roots.
How to use this calculator
- Enter or choose coefficient a (not zero).
- Enter or choose coefficient b.
- Enter or choose coefficient c.
- Select Calculate and review the result and assumptions.
Worked example
For x² − 3x + 2 = 0, the discriminant is 1 and the roots are 1 and 2.
Assumptions and limitations
Coefficient magnitudes are limited to 10¹²; nonzero coefficients smaller than 10⁻¹⁰⁰ are rejected to avoid underflow. Displayed roots are rounded; ill-conditioned equations can lose precision.
Frequently asked questions
What if the discriminant is negative?
The calculator displays the complex-conjugate roots.
Can a be zero?
No. With a equal to zero, the equation is not quadratic.