Answer
$5$.
0 positive real zero.
3 or 1 negative real zeros.
Work Step by Step
Step 1. Based on the given function, we have degree $n=5$, thus the maximum number of real zeros that the polynomial function may have is $5$.
Step 2. As there is 0 sign change in $f(x)$, based on the Descartes’ Rule of Signs, there will be 0 positive real zero.
Step 3. $f(-x)=-x^5+x^4+x^2-x+1$ and there are 3 sign changes in $f(-x)$, thus there may be 3 or 1 negative real zeros.