中世纪数学家阿尔·胡塔里及其代数著作

A Famous mathematician of the Middle Ages Ibn Truk Al Hutalli and his scientific works on quadratic equations

主要研究中世纪著名数学家伊本·土热克·阿尔·胡塔里和他的有关一元二次方程的学术著作,他与同时代的花拉子米一样,研究了一元二次方程的一般解法,并给出了二次方程的求根公式.不同的是他运用判别式来讨论一元二次方程解的情况,指出当判别式小于零时一元二次方程没有实根并给出了严格的几何证明.

In this paper, we mainly studied the life of a famous mathematician Ibn Truk Al Hutalli in the Middle-Ages and his scientific works on quadratic equations. Like al Khowarizmi in the same time, he also studied general solutions, and obtained the formula for roots of quadratic equations. The differeace was that he used the discriminant to discuss the solutions of quadratic equations. Moreover, he presented a strict geometric proof of the fact that the quadratic equations have no real roots when the discriminant less than zero.