If $P(z)$ is a polynomial of degree $n$, then for a subclass of polynomials, Dalal and Govil \cite{DG3} compared the bounds, containing all the zeros, for two different results with two different real sequences $\lambda_k>0$, $\sum_{k=1}^n \lambda_k=1$. In this paper, we prove a more general result, by which one can compare the bounds of two different results with the same sequence of real or complex $\lambda_k$, $\sum_{k=0}^n\abs{\lambda_k}\le 1$. A variety of other results have been extended in this direction, which in particular include several known extensions and generalizations of a classical result of Cauchy \cite{C}, from this result by a fairly uniform manner.