Polynomial Roots Calculator
Enter the coefficients. Leave d empty for a quadratic ax² + bx + c.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Quadratic: x = (−b ± √(b² − 4ac)) ÷ 2a
- Cubic: shift x so the x² term vanishes, then solve with Cardano’s or the trigonometric method
For quadratics with a worked discriminant, use the quadratic equation calculator.
Worked example
x³ − 6x² + 11x − 6 = 0:
Why your number may differ
Roots are rounded to 6 decimal places. Equations of degree 4 and above have no general closed form and are not covered.
Frequently asked questions
How are the roots found?
Quadratics use the quadratic formula. Cubics use a closed-form method (Cardano's or the trigonometric form), which finds all three roots.
What does 0.5 + 0.866i mean?
It is a complex root. Real polynomials always have complex roots in conjugate pairs, so you will see both a + bi and a − bi.
Why must a not be zero?
If the highest coefficient is zero, the polynomial has a lower degree. Move the numbers into the right boxes.