What meaning do multiple real solutions of a truncated virial equation have, if any?
The virial equation is set up for the gas phase only.  The virial coefficients $B$ and $C$ are found from gas phase measurements.

If you get three solutions, I suspect that it is the largest one that you want.  I'd do a trial solution with something like water vapor to see.

Higher order virial equations are problematic since it is exceptionally difficult to determine higher virial coefficients from experimental data.  Higher order virial equations do have theoretical interest, but that's another story.