Polynomial Root Finder

Find all roots of any polynomial. Free online polynomial root calculator.

The Polynomial Root Finder calculates all roots of polynomials of any degree using numerical methods. Enter your polynomial coefficients to find real and complex roots with high precision. This versatile tool handles polynomials that cannot be solved algebraically, using Newton's method and deflation techniques.

Common use cases

  • Signal processing (filter design)
  • Control systems (pole-zero analysis)
  • Numerical analysis
  • Scientific research
  • Mathematical exploration

How to use

  1. Enter polynomial degree
  2. Input coefficients (highest to lowest degree)
  3. Click find roots
  4. View all roots with precision
  5. Verify by substitution

FAQ

What degrees are supported?

Any degree, though high degrees may have precision limitations. Practical limit around degree 20.

How accurate are the roots?

Numerical methods provide roots to floating-point precision, typically 10-15 significant digits.

Are complex roots shown?

Yes, all roots including complex ones are displayed in a+bi form.

What method is used?

Combination of techniques: Aberth-Ehrlich method, Newton-Raphson refinement, and deflation.