Three researchers from Bristol University are seeking to develop methods for analysing the distribution of integer solutions to polynomial equations. How do you know when a polynomial equation has ...

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).

Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots.

Iterative methods for solving nonlinear equations and finding polynomial zeros are essential tools in mathematics and engineering. These methods aim to approximate the roots of equations ...

Orthogonal polynomials and Painlevé equations are two significant areas of study in mathematics that intersect in various ways. Orthogonal polynomials are sequences of polynomials that are ...