Answer
3 or 1 positive real zeros.
no negative real zeros.
Work Step by Step
Step 1. Given the function $f(x)=-2x^3+x^2-x+7$, we can see that $f(x)$ has 3 sign changes. Thus, based on Descartes’s Rule of Signs, the function may have 3 or 1 positive real zeros.
Step 2. Testing the function $f(-x)=2x^3+x^2+x+7$, we can see that $f(-x)$ has 0 sign changes. Thus, based on Descartes’s Rule of Signs, the function has no negative real zeros.