Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 377: 36

3 or 1 positive real zeros. no negative real zeros.

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.