Polynomial equation is an equation of the form *f(x) = a _{0 }+a_{1 }·x+a_{2 }·x^{ 2}+...+a_{n }·x^{ n} = 0*.
Although encountered less frequently than systems of linear equations (or nonlinear systems),
polynomial equations still arise in some situations and still need solvers.

ALGLIB has polynomial solver which utilizes companion matrix method (eigendecomposition of NxN matrix) and returns both real and complex roots of the polynomial. This functionality is implemented by polynomialsolve function of polynomialsolver subpackage.

**Note #1**

Polynomial equations are inherently unstable. It is very hard to find precise solutions even for moderate values of *N* (even *N=10* can be problematic).
If your problem involves solution of high-degree polynomial equation, we recommend you to try reformulating it in a way which avoids polynomials.

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