Fourier-Budan Theorem

For any real  and  such that , let  and  be real polynomials of degree , and  denote the number of sign changes in the sequence . Then the number of zeros in the interval (each zero counted with proper multiplicity) equals  minus an even nonnegative integer.

REFERENCES:

Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros.New York: Wiley, p. 443, 1988.