Primes and Quadratics

Question

Let $a$,$b$ $\in$ $\Bbb N$ such that the equations $$x^2+ax+b$$ $$x^2+bx+a$$ have all of their roots as integers. Find all $a$ and $b$.

My Approach I tried using Vieta's Relations but the process got too much complicated and I gave up. Any help?