Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 294: 107

Zeros: $ \frac{-5\pm\sqrt {13}}{6}$ x-intercepts $ \frac{-5\pm\sqrt {13}}{6}$.

Step 1. Zeros: $f(x)=0 \Longrightarrow 3x^2+5x+1=0 \Longrightarrow x=\frac{-5\pm\sqrt {25-4(3)}}{2(3)}=\frac{-5\pm\sqrt {13}}{6}$ Step 2. The x-intercepts are the same as the zeros $x=\frac{-5\pm\sqrt {13}}{6}$.