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Find all real and complex roots of a polynomial from a coefficient list using a numerical root finder
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Polynomial Roots Calculator is a numerical math tool designed to find all real and complex roots of a polynomial equation. By simply entering a comma-separated list of coefficients, you can quickly calculate the zeros of cubic, quartic, or higher-degree polynomials without manual algebraic solving.
Background
Needs to find the roots of the equation x^3 - 6x^2 + 11x - 6 = 0 for an algebra assignment.
Problem
Factoring cubic equations manually is time-consuming and prone to arithmetic errors.
How to use
Enter '1, -6, 11, -6' into the coefficients field and keep the default 6 decimal places.
Coefficients: 1, -6, 11, -6Outcome
The tool instantly returns the real roots: 1, 2, and 3.
Background
Analyzing a system with the characteristic equation x^4 - 1 = 0.
Problem
Needs to identify both the real and imaginary poles of the system to determine stability.
How to use
Input '1, 0, 0, 0, -1' to account for the missing x^3, x^2, and x terms.
Coefficients: 1, 0, 0, 0, -1Outcome
Enter them as a comma-separated list in descending order of degree. Include zeros for any missing terms. For example, x^3 - 1 would be entered as '1, 0, 0, -1'.
Yes, the numerical root finder calculates both real and complex roots of the polynomial.
The tool can handle high-degree polynomials, limited only by the numerical stability of the root-finding algorithm and the maximum iteration limit.
It limits how many times the numerical algorithm attempts to converge on a root. Increase this value up to 500 if the tool struggles to find roots for complex polynomials.
The algorithm relies on the position of the coefficient in the list to determine its power. Omitting a zero changes the degree of all subsequent terms.
The calculator outputs the real roots (1, -1) and the complex roots (i, -i).