What is the Polynomial Solver?
Find all roots of a polynomial equation up to degree 6. Enter coefficients from the leading term down to the constant, or type a full equation like x³ − 6x² + 11x − 6 = 0. Linear and quadratic equations use exact formulas; cubic through sextic polynomials are solved numerically with Durand–Kerner iteration. Results include standard form, all real and complex roots, and solution steps. Free, private, and instant in your browser.
How to use the Polynomial Solver
- Choose Coefficients mode or Equation mode.
- Enter the degree and coefficients, or type a polynomial equation with =.
- Set the variable letter if it is not x.
- Read all roots, degree, and solution method.
- Copy the full solution for homework or notes.
Common use cases
- Finding roots of x³ − 6x² + 11x − 6 = 0 for algebra homework
- Solving quartic equations like x⁴ − 5x² + 4 = 0
- Checking numerical roots of degree 5 or 6 polynomials
Frequently asked questions
- What degree polynomials are supported?
- Degrees 1 through 6. The leading coefficient must be non-zero.
- How are higher-degree roots computed?
- Degree 1 and 2 use exact algebraic formulas. Degrees 3–6 use Durand–Kerner numerical iteration, which finds real and complex roots.
- How do I enter powers?
- Use ^ for exponents, e.g. x^3 or x^3 - 2x + 1 = 0. Unicode superscripts like x³ also work.
- Can I enter terms on both sides of =?
- Yes. The solver combines both sides into standard form automatically.
