Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 352: 48

See explanations.

Step 1. Given $f(x)=3x^2-x-4$, for $x=1$, we have $f(1)=3(1)^2-(1)-4=-2\lt0$ Step 2. For $x=2$, we have $f(2)=3(2)^2-(2)-4=6\gt0$ Step 3. As $f(1)$ and $f(2)$ have opposite signs, based on the intermediate value theorem, there is a real zero between 1 and 2.