Let's say I truncate the virial equation after the third term for use as my equation of state:
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?