# Descartes rule of signs

Hi,

Does the Descartes rule of signs count multiplicities when giving its upper bound for roots? That is if I have 3 sign changes, does that mean there is a maximum of 3 positive roots counting multiplicities or not counting multiplicities?

Thanks

Each root, even if the same, is counted separately.

HallsofIvy
For example, $(x- 2)^3= x^3- 6x^2+ 12x- 8= 0$ has three sign changes and three positive roots- counting "2" as a triple root.
But the number of sign changes of $(x- 2)^2= x^2- 4x+ 4= 0$ is 2 so Descarte's rule of signs say the number of positive roots is 2 or 0. And it clearly is not 0.