Find all rational roots of a polynomial equation
The paper Computing Real Roots of Real Polynomials by Sagraloff and Mehlhorn from 2015 provides an almost optimal algorithm and references for simpler algorithms that might be used in practice. The CGAL library (in version 4.9) for example uses the method developed by Arno Eigenwillig in his PhD thesis Real Root Isolation for Exact and Approximate Polynomials Using Descartes' Rule of Signs.