The intertwined study of orthogonal polynomials and Painlevé equations continues to be a fertile area of research at the confluence of mathematical analysis and theoretical physics. Orthogonal ...

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. What type of ...

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 \(f(x) = 0\).

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

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 ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

A mathematician has solved a 200-year-old maths problem after figuring out a way to crack higher-degree polynomial equations without using radicals or irrational numbers. The method developed by ...

In a boon to algebra students everywhere, a professor at Carnegie Mellon University has devised a simpler and more efficient way to solve problems involving the quadratic equation. The new method was ...

For centuries, one of algebra’s oldest puzzles has remained unsolved—how to find exact answers for higher-degree polynomials, where the variable is raised to the fifth power or more. Mathematicians ...

A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...