z n − pz + q = 0. .....(1) The usual method of solution by means of a fixed curve and varying line is to draw the curve y = z n , 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.