Isolating the polynomial roots with all zeros real

It is known that, if all the roots of a polynomial are real, they can be localizing, using a set of intervals, which contain the arithmetic average of the roots. The aim of this paper is to give an original method for evaluating and improving the 'polynomial minimum root separation' results, for the polynomials having all real roots. We use Hadamard inequality and new original inequalities. Also we make some considerations about the cost for isolate the polynomial roots. Our method is based on the construction of new intervals containing only one root of the polynomial.