Precalculus (6th Edition) Blitzer

Step 1. Given the function $f(x)=x^3+7x^2+x+7$, we can see that $f(x)$ has no sign change. Thus, based on Descartes’s Rule of Signs, there are no positive real zeros. Step 2. Test the function $f(-x)=-x^3+7x^2-x+7$. 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 negative real zeros.