Polynomial Equation Solver (Numerical Roots)

Enter coefficients from the highest degree and get every root of an n-degree polynomial, including complex roots, via the Durand-Kerner method.

Input

Enter the coefficients from the highest degree to compute all roots of an n-degree equation numerically, including complex roots.

Coefficients (highest degree first)

Separate by commas, spaces, or line breaks. Include 0 for any missing power.

x⁴ - 5x² + 4 = 0

Roots of the equation

x1 = -2

x2 = -1

x3 = 1

x4 = 2

Degree

Real roots

Complex roots

Roots detail

All roots are numerical solutions from the Durand-Kerner simultaneous iteration.

Enter coefficients from the highest degree first, separated by commas, spaces, or line breaks. For example x to the fourth minus 5x squared plus 4 is entered as 1, 0, -5, 0, 4.
Always include a 0 for any missing power so positions stay aligned.
Every root is computed numerically by the Durand-Kerner (Weierstrass) simultaneous iteration. Accuracy can drop for repeated or closely spaced roots.
Roots with zero imaginary part are counted as real, the rest as complex. Because the coefficients are real, complex roots appear in conjugate pairs.
Displayed values are rounded to 8 decimal places.

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