Sturm Theorem

The number of Real Roots of an algebraic equation with RealCoefficients 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 theSturm Chains formed for the interval ends.

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.

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