What meaning do multiple real solutions of a truncated virial equation have, if any? Let's say I truncate the virial equation after the third term for use as my equation of state:

$${P\over\rho RT}=1+B\rho+C\rho^2$$

I have tabulated values for $B(T)$ and $C(T)$.  I know $P$ and $T$ and want to solve for $\rho$.  The equation is cubic in $\rho$ meaning I could potentially have three real solutions.  I suspect that since the virial equation is intended to calculate the densities of vapors or supercritical gasses at relatively low pressures, that the lowest real root is the "real world" value.  Is this correct?  Do the other real values, if they exist, have any meaning?  Can this be generalized to higher order virial expansions?
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.