This paper is concerned with the relationship between the sum of roots with positive real parts (SORPRP) of an even polynomial and the polynomial spectral factor of the even polynomial. The SORPRP and its relationship to Grobner bases are firstly reviewed. Then it is shown that the system of equations satisfied by the coefficients of the polynomial spectral factor is directly related to a Grobner basis. It is then demonstrated by means of an H-2 optimal control problem that the above fact can be used to facilitate guaranteed accuracy computation.