Assume $n$ is a positive integer and integer $a$ is the root of the equation $$x^4+3ax^2+2ax-2\times 3^n=0.$$Find all $n$ and $ a$ that satisfy the conditions.
Source: China Northern MO 2008 p5 CNMO
Tags: algebra, polynomial, number theory
Assume $n$ is a positive integer and integer $a$ is the root of the equation $$x^4+3ax^2+2ax-2\times 3^n=0.$$Find all $n$ and $ a$ that satisfy the conditions.