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 ![[alpha,beta]](/images/equations/Fourier-BudanTheorem/Inline9.svg)
(each zero counted with proper multiplicity) equals
minus an even nonnegative integer.
Fourier-Budan Theorem
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References
Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, p. 443, 1988.Referenced on Wolfram|Alpha
Fourier-Budan TheoremCite this as:
Weisstein, Eric W. "Fourier-Budan Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Fourier-BudanTheorem.html