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 ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

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 ...

Mathematics of Computation, Vol. 33, No. 148 (Oct., 1979), pp. 1251-1256 (6 pages) A polynomial representation of the hybrid methods for solving ordinary differential equations is presented. The ...

When you buy through links on our articles, Future and its syndication partners may earn a commission. Mathematicians have solved a longstanding algebra problem, providing a general solution for ...

We consider solving integral equations on a piecewise smooth surface S in R3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical ...

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 built an algebraic solution to an equation that was once believed impossible to solve. The equations are fundamental to maths as well as science, where they have broad applications ...