|
|
|
The number of Real Roots of an algebraic equation with Real Coefficients whose Real Roots are simple over an interval, the endpoints of which are not Roots, is equal to the difference between the number of sign changes of the Sturm Chains formed for the interval ends.
See also Sturm Chain, Sturm Function
References
Dörrie, H. ``Sturm's Problem of the Number of Roots.'' §24 in
100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 112-116, 1965.
Rusin, D. ``Known Math.'' http://www.math.niu.edu./~rusin/known-math/polynomials/sturm.