Fallibility of analytic roots of cubic equations of state in low temperature region

It is showed by several examples that, in low temperature region, the analytical solutions of cubic equation of state (EOS) lead to irrational results, while the iterative solutions of cubic EOS by using the Newton–Raphson method produce valid results. Errors caused by the limitation of significant figures of the computer languages are revealed, and a magnification of errors is defined which is a main factor bringing out the irrational results of the analytical solution of cubic EOS.