Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for the Wolfram Language. Routinely handling both dense and sparse polynomials with thousands of terms, the Wolfram Language can represent results in terms of numerical approximations, exact radicals or its unique symbolic Root object constructs.

Solve — find generic solutions

Roots — roots of a univariate polynomial

Reduce — reduce a general polynomial system

SolveValues, NSolveValues — directly gives solution vectors

Solutions in Radicals

Root  ▪  Cubics  ▪  Quartics  ▪  ToRadicals

Root Isolation

CountRoots — count roots in an interval

RootIntervals  ▪  IsolatingInterval

Numerical Approximations

NSolve  ▪  NRoots  ▪  FindRoot