Budan's theorem
= Budan's theorem
{wiki=Budan's_theorem}
Budan's theorem is a result in algebra that provides a method for determining the number of real roots of a polynomial within a specific interval. Specifically, it relates to the evaluation of the signs of the polynomial and its derivatives at the endpoints of the interval. The theorem can be stated as follows: 1. Consider a polynomial \\( P(x) \\) of degree \\( n \\) and its derivative \\( P'(x) \\).