Answer
$5$.
1 positive real zero.
0 negative real zero.
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 1 sign change in $f(x)$, based on the Descartes’ Rule of Signs, there will be 1 positive real zero.
Step 3. $f(-x)=3x^5+4x^4+2$ and there is no sign change in $f(-x)$, thus there will be 0 negative real zero.
