How to determine if this filter is stable
Zeroes of H don't play any role in stability.

For the filter to be stable, you have to ensure that all poles of H are inside the unit circle, i.e. their modulus (distance of the pole from the origin of the Z-plane) is less than one.

In your case the poles are the zeroes of the polynomial at denominator, i.e the roots of the equation \$z^2 + 3.24 = 0\$. Solve this and verify whether its roots \$z_k\$ are such that

\$\left| z_k \right| &lt; 1 \quad \forall k\$.