Geometrical solutions of some quadratic equations with non-real roots

Abstract

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax 2 + bx + c = 0, a p 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the quadratic equation ax 2 + bx + c = 0, a p 0, when a,b,c ] R, the set of real numbers, are presented. Case II deals with the geometrical solutions of the quadratic equation ax 2 + bx + c = 0, a p 0, when b ] R, the set of real numbers; and a,c ] C, the set of complex numbers. Finally, the solutions of the quadratic equation ax 2 + bx + c = 0, a p 0, when a,c ] R, the set of real numbers, and b ] C, the set of complex numbers, are presented in case III.