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Pure mathematics, Applied mathematics
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.
Prodanov, E. (2022). On Newton's Rule of Signs. Technological University Dublin. DOI: 10.21427/KGAN-TS20