Budan's theorem

In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent.

A similar theorem was published independently by Joseph Fourier in 1820. Each of these theorems is a corollary of the other. Fourier's statement appears more often in the literature of the 19th century and has been referred to as Fourier's, Budan–Fourier, Fourier–Budan, and even Budan's theorem.

Budan's original formulation is used in fast modern algorithms for real-root isolation of polynomials.