A Graphical Treatment of Algebraic Equations

Extract

Recent notes in the Gazette on the discrimination of the roots of the cubic and quartic suggest that the following method, if not new, is not so widely known as it deserves to be. The only tool required in addition to a facility in reading graphs is a knowledge of differentiation and so the method lies within the scope of the work done by evening technical students and others whose grasp of ordinary algebra is so weak as to prevent their following up the normal methods of discussing the roots of equations. The treatment is also sufficiently general to be of real interest to a type of student whose body of mathematical knowledge is always, from the pressure of other subjects, threatening to disintegrate into a collection of scraps of special methods each applicable to one type of problem. The method yields very easily the discriminants for the quadratic and cubic and it also offers a nomographic device for the solution of numerical equations. In practice, however, even with large scale drawings, students are not able to obtain results as accurate as they can readily get by other graphical methods.