[[Analysis MOC]]
# Descarte's rule of signs

For a [[Polynomial ring|polynomial]] $f(x) \in \mathbb{R}[x]$,
let $\opn c(f(x))$ be the number of sign changes in the sequence of coëfficients,
and let $\opn r(f(x))$ be the number of real roots. #m/thm/anal Then
$$
\begin{align*}
\opn r(f(x)) = \opn c(f(x)) - 2k
\end{align*}
$$
for some $k \in \mathbb{N}_{0}$.


> [!missing]- Proof
> #missing/proof
#
---
#state/develop | #lang/en | #SemBr