1257 Words6 Pages

Abstract—Research compiled from video lectures and articles retrieved from the internet is the basis for the findings in this article related to solving a cubic equation. The noteworthy mathematicians and their contributions to the solution and their understanding of the cubic equation is included. Also included is an example of a cubic equation solved using Descartes’ Factor Theorem.
Index Terms—complex number, cubic equation, Descartes, Riehmen Sphere, Tartaglia
Introduction
Building on the successes of their ancient predecessors the mathematicians of the European Renaissance searched for an algebraic solution to the cubic equation. The ancient Egyptian and Babylonian mathematicians produced solutions for the linear and quadratic equations. By 628, Brahmagupta, the Indian mathematician, developed the general quadratic formula for solving a quadratic equation. In the eighth century, the great Persian mathematician, Al-Kharizmi, offered a solution to the quadratic equation by completing the square. But solving the cubic equation or finding the zeroes of the polynomials of degree three evaded the great mathematicians. Omar Khayyan, the Islamic poet, astronomer, and mathematician attempted to find a general algebraic solution to the cubic equation but was able to only offer a geometric solution for a specific cubic equation. During the Renaissance, Tartaglia, Cardano, Viete, Fermat, and Descartes, made advances in solving the cubic equation. Later, Newton and Riemann would

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