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A Graphic Solution of the Equation

Published online by Cambridge University Press:  03 November 2016

A. Lodge
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Extract

zn − pz + q = 0. .....(1)

The usual method of solution by means of a fixed curve and varying line is to draw the curve y = zn, and find where it is cut by the line y=pz − q.

The following method is quicker, and has some aspects of theoretic interest to recommend it. It consists in taking p, q as coordinates, and in drawing the curve given by the parametric equation

2

which is the condition that the given equation (1) shall have equal roots.

Type
Research Article
Information
The Mathematical Gazette , Volume 7 , Issue 103: Special Commemorative Issue , 1913 , pp. 41 - 45
Copyright
Copyright © Mathematical Association 1913

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