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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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 $p(-x)$ or less than the first following even number.

For example: $f(x)=-x_{2}+3x−2.$ 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 $f(x)=-(x−1)(x−2) $ 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.