### Quadratic Polynomials with Rational Roots and Integer Coefficients in Arithmetic Progression

#### Abstract

In this paper, we first give conditions on the integer coefficients $a,b,c$ of the quadratic equations of the form $ax^2+bx+c=0$ and $ax^2 +bx-c=0$ 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.

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