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DOI	10.35834/mjms/1513306828
	GEOMETRY OF POLYNOMIALS WITH THREE ROOTS
	Frayer, Christopher
通讯作者	Frayer, C
来源期刊	MISSOURI JOURNAL OF MATHEMATICAL SCIENCES
ISSN	0899-6180
出版年	2017
卷号	29 期号:2 页码:161-175
英文摘要	Given a complex-valued polynomial of the form p(z) = (z-1)(k) (z-r(1))(m) (z-r(2))(n) with broken vertical bar r(1)broken vertical bar = broken vertical bar r(2)broken vertical bar = 1; k,m,n is an element of N and m not equal n, where are the critical points? The Gauss-Lucas Theorem guarantees that the critical points of such a polynomial will lie within the unit disk. This paper further explores the location and structure of these critical points. Surprisingly, the unit disk contains two 'desert' regions in which critical points cannot occur, and each c inside the unit disk and outside of the desert regions is the critical point of exactly two such polynomials.
英文关键词	geometry of polynomials critical points Gauss-Lucas Theorem
类型	Article
语种	英语
收录类别	ESCI
WOS记录号	WOS:000418031400004
WOS类目	Mathematics
WOS研究方向	Mathematics
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/332411
作者单位	[Frayer, Christopher] Univ Wisconsin Platteville, Dept Math, Platteville, WI 53818 USA
推荐引用方式 GB/T 7714	Frayer, Christopher. GEOMETRY OF POLYNOMIALS WITH THREE ROOTS[J],2017,29(2):161-175.
APA	Frayer, Christopher.(2017).GEOMETRY OF POLYNOMIALS WITH THREE ROOTS.MISSOURI JOURNAL OF MATHEMATICAL SCIENCES,29(2),161-175.
MLA	Frayer, Christopher."GEOMETRY OF POLYNOMIALS WITH THREE ROOTS".MISSOURI JOURNAL OF MATHEMATICAL SCIENCES 29.2(2017):161-175.

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