From Vieta's Formulas, I got:
$a=2r+k$
$b=2rk+r^2+s^2$
$65=k(r^2+s^2)$
Where $k$ is the other real zero.
Then I split it into several cases: $r^2 + s^2 = 1, 5, 13, 65$ then:
For case 1: $r = \{2, -2, 1, -1 \}$
$\sum a = 2(\sum r) + k \implies a = 13$
Then for case 2: $r^2 + s^2 = 13$, it...