Some more comments on "On the Routh-Hurwitz criterion"

Recently it was pointed out that the Routh-Hurwitz criterion may fail to give correct root distribution in certain situations. It is demonstrated in this correspondence that the Routh-Hurwitz criterion itself can be used to find out the root distribution correctly in the left-half plane (LHP), on the imaginary axis and in the right-hand plane (RHP) without recourse to finding the common factor between the even and odd parts of a polynomial.