期刊
AMERICAN MATHEMATICAL MONTHLY
卷 127, 期 3, 页码 258-262出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/00029890.2020.1697589
关键词
MSC
类别
资金
- Spanish Ministerio de Ciencia, Innovacion e Universidades [DPI2015-65472-R]
- ERFD (European Regional Development Fund)
The midpoints between roots provide the key to understanding the geometry, in the complex plane, behind the roots of a quartic polynomial. In reduced form (i.e., with no cubic term), midpoints come in three pairs, with opposite signs, as solutions to a resolvent cubic. At any midpoint, a startlingly simple expression of the polynomial derivative indicates the vectors from the midpoint to the corresponding pair of roots. This approach simplifies Euler's method for solving the quartic, since there is no need to make a suitable choice of the plus or minus signs in the pairs of midpoints.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据