Answer
(a) $\{-2,0\ (multiplicity\ 2),4\}$
(b) $[-2,4]$
(c) $(-\infty,-2]U[4,\infty)$
Work Step by Step
(a) Graph the function $f(x)=-x^4+2x^3+8x^2$ as shown in the figure. We can identify the zeros as $x=-2,0\ (multiplicity\ 2),4$ or $\{-2,0\ (multiplicity\ 2),4\}$
(b) For $f(x)\ge 0$, we can identify the intervals as $[-2,4]$
(c) For $f(x)\le 0$, we can identify the intervals as $(-\infty,-2]U[4,\infty)$
