Document Type
Article
Rights
Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence
Disciplines
Pure mathematics, Applied mathematics
Abstract
Analysing the cubic sectors of a real polynomial of degree n, a minor modification of Newton’s Rule of signs is proposed with which stricter upper limits on the number of real roots can be found. A new necessary condition for reality of the roots of a polynomial is also proposed. Relationship between the quadratic elements of the polynomial is established through its roots and those of its derivatives. Some aspects of polynomial discriminants are also discussed.
DOI
https://doi.org/10.21427/kgan-ts20
Recommended Citation
Prodanov, E. (2022). On Newton's Rule of Signs. Technological University Dublin. DOI: 10.21427/KGAN-TS20
Publication Details
Analysing the cubic sectors of a real polynomial of degree $n$, a minor modification of Newton's Rule of signs is proposed with which stricter upper limits on the number of real roots can be found. A new necessary condition for reality of the roots of a polynomial is also proposed. Relationship between the quadratic elements of the polynomial is established through its roots and those of its derivatives. Some aspects of polynomial discriminants are also discussed.