Location of the zeros of orthogonal polynomials with an automatic procedure I

We propose a new algorithm for localising the zeros of a family of orthogonal polynomials {Pn}n>0N. We start with an old theorem which gives the exact positions of the extremal zeros of the polynomial PN. But applying this old result, we may have difficulties to obtain these zeros. We are going to show, how to modify this theorem in order to obtain a new method which is simpler and more effective. Hence how to build an automatic procedure to compute these extremal zeros.