🌀Polynomial Root Finder
Find all real and complex roots of any polynomial, with a graph and verification.
Free Polynomial Root Finder
Our free polynomial root finder computes every root — real and complex — of a polynomial equation from its coefficients, using the Durand-Kerner iterative method. It works for any degree, not just quadratics and cubics, and shows each root's real and imaginary parts along with a verification check confirming the polynomial evaluates to (approximately) zero there.
Enter coefficients highest-degree-first, separated by commas — for example 1, -6, 11, -6 for x³ − 6x² + 11x − 6. Real roots are plotted on a graph of the polynomial so you can see exactly where the curve crosses the x-axis, while complex roots (which don't appear on the real graph) are listed alongside them as conjugate pairs.
Built for algebra and precalculus students solving polynomial equations, and for anyone who needs a fast, reliable check of factored or numerically-approximated roots. No sign-up, no downloads — just instant results.
About the Polynomial Root Finder
Features
Any degree up to 8
Handles quadratics, cubics, quartics, and higher-degree polynomials.
Real and complex roots
Every root is found and labeled, including conjugate complex pairs.
Live graph
Real roots are plotted where the polynomial curve crosses the x-axis.
Quick examples
One-click sample polynomials to see how the tool works.
Frequently Asked Questions
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.