Algebra
Polynomial Solver
Enter polynomial coefficients and receive all complex roots using the Durand–Kerner method.
polynomialrootsequation solver
Polynomial Solver
Enter coefficients (highest degree first) to approximate complex roots.
Degree
3
Root 1
1
Root 2
3
Root 3
2
General polynomial
The calculator normalizes the polynomial a₀xⁿ + a₁xⁿ⁻¹ + … + aₙ and iteratively refines the roots until convergence.
How to use
- List coefficients from highest degree to constant term.
- Separate coefficients with commas or spaces.
- Review each root along with its complex form.
Example
Input: Coefficients = 1, −6, 11, −6
Output: Roots: x = 1, 2, 3
FAQ & notes
How accurate are the roots?
Roots converge to double-precision accuracy for well-conditioned polynomials. The output rounds to eight decimals for readability.
Does the order of coefficients matter?
Yes. Always supply coefficients starting with the highest power of x down to the constant term.