For a polynomial function $p(x)$ written in standard form:

• The number of positive real zeros is equal to the number of sign changes in $p(x)$ or less than the first following even number.
• The number of negative real zeros is equal to the number of sign changes in $p(\text{-}x)$ or less than the first following even number.

For example: $$f(x)=\text{-}{x}^2+3x-2.$$ According to the rule, the number of positive real zeros can be either $2,$ since there are two changes in sign, or, $0$ because one less than the following even number is still $0.$

The function can be factored to $$\begin{array}{r}f(x)=\text{-}(x-1)(x-2)\end{array}$$ and using the zero product property the zeros are given by $x=1$ and $x=2.$ Thus, $f(x)$ has two real positive zeros as stated by Discartes' rules of signs.