We describe an alternative approach to some results of Vassiliev on spaces of
polynomials, by using the scanning method which was used by Segal in his
investigation of spaces of rational functions. We explain how these two
approaches are related by the Smale-Hirsch Principle or the h-Principle of
Gromov. We obtain several generalizations, which may be of interest in their
own right.Comment: 29 pages, AMS-Te