Counting complex roots in polynomials with real coefficients

A three-step procedure is presented which converts an nth-order polynomial into a (2n + 1)th-order polynomial whose number of right-hand plane poles equals the number of complex roots present in the original polynomial. It is shown that these three steps can be carried out by a simple manipulation of the coefficients of the original polynomial, permitting the first three rows of the Routh criterion used to test the transformed polynomial to be written directly. The procedure is illustrated by two examples.