Frequently Asked Questions
Everything you need to know about the Polynomial Root Finder.
How do I enter a polynomial?
Enter its coefficients from highest degree to lowest, separated by commas, e.g. 1, -6, 11, -6 for x³ − 6x² + 11x − 6.
Does it find complex roots?
Yes. It finds all real and complex roots using the Durand-Kerner method, which converges on every root of the polynomial simultaneously.
What's the maximum degree supported?
Degree 8, to keep the numerical iteration stable and accurate.
Why don't complex roots show on the graph?
The graph only plots real x and y values, so complex roots (which have a non-zero imaginary part) can't be shown as x-axis crossings. They're listed in the roots section instead.
How accurate are the roots?
Roots are refined until the change between iterations is below 1e-12, which gives results accurate to several decimal places for well-conditioned polynomials.
Can the leading coefficient be zero?
No — a zero leading coefficient would make it a lower-degree polynomial; remove that term instead.
Do complex roots always come in pairs?
Yes, for polynomials with real coefficients, complex roots always occur as conjugate pairs (a + bi and a − bi).
What method does it use?
The Durand-Kerner (Weierstrass) iterative method, which updates all root estimates at once rather than finding and deflating one root at a time.
Is my data stored?
No; all computation happens locally in your browser.
Is it free?
Completely free, no sign-up or limits.