Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes ...

Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

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 ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

First, we need to find which number when substituted into the equation will give the answer zero. \(f(1) = {(1)^3} + 4{(1)^2} + (1) - 6 = 0\) Therefore \((x - 1)\)is a factor. Factorise the quadratic ...

In this article we consider matrix factorizations of a polynomial where the two matrices appearing in the factorization are the same, which we call "matrix square roots." The main result is that any ...

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 ...

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 ...

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 ...