Abstract
The most basic and important theorem concerning polynomials is the Fundamental Theorem of Algebra. This theorem, which tells us that every polynomial factors completely over the complex numbers, is the starting point for this book. Some of the intricate relationships between the location of the zeros of a polynomial and its coefficients are explored in Section 2. The equally intricate relationships between the zeros of a polynomial and the zeros of its derivative or integral are the subject of Section 1.3. This chapter serves as a general introduction to the body of theory known as the geometry of polynomials. Highlights of this chapter include the Fundamental Theorem of Algebra, the Eneström-Kakeya theorem, Lucas’ theorem, and Walsh’s two-circle theorem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Borwein, P., Erdélyi, T. (1995). Introduction and Basic Properties. In: Polynomials and Polynomial Inequalities. Graduate Texts in Mathematics, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0793-1_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0793-1_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94509-5
Online ISBN: 978-1-4612-0793-1
eBook Packages: Springer Book Archive