## Precalculus (6th Edition) Blitzer

Step 1. Given the function $f(x)=5x^3-3x^2+3x-1$, 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 $f(-x)=-5x^3-3x^2-3x-1$, we can see that $f(-x)$ has 0 sign changes. Thus, based on the Descartes’s Rule of Signs, the function has no negative real zeros.