Answer
See explanations.
Work Step by Step
Step 1. Given $f(x)=x^5-3x^4-2x^3+6x^2+x+2$, we have
$f(1.7)=(1.7)^5-3(1.7)^4-2(1.7)^3+6(1.7)^2+(1.7)+2\approx0.36\gt0$
Step 2. Similarly, we have
$f(1.8)=(1.8)^5-3(1.8)^4-2(1.8)^3+6(1.8)^2+(1.8)+2\approx-1.02\lt0$
Step 3. Based on the Intermediate Value Theorem, there is a zero in the given interval.