Answer
$(-\infty,-\frac{4}{3}]U[1,\infty)$
Work Step by Step
Step 1. Graph $f(x)=3x^2+x-4$ as shown in the figure.
Step 2. The solutions to $f(x)=0$ can be found from x-intercepts as $x=-\frac{4}{3},1$
Step 3. The interval for $f(x)\ge0$ can be identified from the graph as $(-\infty,-\frac{4}{3}]U[1,\infty)$
