The negative Routh test and its application to the cases of vanishing leading elements and imaginary roots
J. F. Feinstein · IEEE Transactions on Automatic Control · 1985
The ordinary Routh test furnishes in a straightforward manner the numberr_{+}of positive roots of a polynomial of degreen. A modification that allows one to obtain the numberr_{-}of negative roots in the same way is presented. Thus, the number roof (purely) imaginary roots is immediately found asn-(r_{+}+r_{-}). The modified test is especially useful when there is a first column vanishing element.