IT is well known that for any real coefficient polynomial f(x) of degree n,how to determineits number of real zero points is a very important problem in theory of polynomial,as well as inapplications in mathematics,mechanics,physics and other subjects.The way to solve thisproblem by using Euclidean mutual division as pointed out by Sturm is not simple and conve-nient for us to use the theoretic analyses for the above problem because the relation between