Quadratic Polynomials with Rational Roots and Integer Coefficients in Arithmetic Progression

Aniruth Phon-On, Rattikan Saelim

Abstract

In this paper, we first give conditions on the integer coefficients a,b,c of the quadratic equations of the form ax² + bx + c = 0 and ax² + bx − c = 0 so that their solutions are rational. Moreover, the coefficients $a,b,c$ are in an arithmetic progression with a common difference d Then, some interesting properties of those rational solutions are shown. Finally, the programming codes in scilab are given in order to generate those coefficients once the common difference $d$ is given.