A Recurrence Relation Sequence of Polynomials having Real Root

Abstract

A recurrence relation is method in mathematics in which every problem divided in sub-problems.  The main area of research which is focused in this article is Number theory. Number theory is also known as higher arithmetic. Reducibility is very important topic of polynomial ring. In this paper author define a special recurrence relation sequence of polynomials having at least one real root. If a polynomial cannot be factorized into polynomials over a ring then polynomial called the irreducible polynomial over that ring. Authors define a special relationship between ring theory and number theory. Authors give a special recurrence relation sequence of polynomials. Authors give special recurrence relation formula with special initial terms such that we will find using this formula infinitely polynomials such that all have at least one real root. Recurrence relation is very useful topic of mathematics and many problems of real life may be solved by recurrence relations but in recurrence relation. In this paper we define a special recurrence relation sequence of polynomials in which all terms have at least one real root.