応用および計算数学ジャーナル

Semi Analytical Approach for Establishing the Two Real Roots of Sextic Polynomial

Abstract

Shebl SA

Zeros of polynomial equations are analytically hard to be determined beyond the special cases of the quartic equations. Under some particular conditions, quintic and sextic polynomial equations may be solved iteratively. This paper presents analytical-graphical solution for accomplishing zeros of particular sextic polynomial equation of two real zeros. The concerned polynomial has been modeled geometrically as the radical problem in geodesy which is the geodetic height of a point on the terrain surface of the earth. The earth’s model to be adopted is the triaxial ellipsoidal surface. The achieved solution may be utilized as initial values for a convenient and convergent iterative process.