Answer
2 or 0 positive real zeros.
1 negative real zero.
Work Step by Step
1. There are two sign changes in $f(x)$, thus there may be 2 or 0 positive real zeros.
2. $f(-x)=2x^3+6x^2+7x-8$, there is one sign change in $f(-x)$, thus there will be 1 negative real zero.
