Problem

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Tags: quadratics, number theory



Polly can do the following operations on a quadratic trinomial: 1) Swapping the places of its leading coefficient and constant coefficient (swapping $a_2$ with $a_0$); 2) Substituting (changing) $x$ with $x-m$, where $m$ is an arbitrary real number; Is it possible for Polly to get $25x^2+5x+2014$ from $6x^2+2x+1996$ with finite applications of the upper operations?