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. What type of ...

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 ...

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 ...

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 ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...

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 ...

Observations on nodal and loop analysis that can save a fair amount of scribbling of equations when using Kirchhoff's laws. In a previous Idea for Design, Anshi Chen outlined a method for analyzing ...

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 ...

Equations, like numbers, cannot always be split into simpler elements. Researchers have now proved that such “prime” equations become ubiquitous as equations grow larger. Prime numbers get all the ...