# Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 377: 35

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

#### Work Step by Step

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.

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