Answer
(a) $\{-3\ (multiplicity\ 2), 0,2\}$
(b) $\{-3\}U[0,2]$
(c) $(-\infty,0]U[2,\infty)$
Work Step by Step
(a) Graph the function $f(x)=-x^4-4x^3+3x^2+18x$ as shown in the figure. We can identify the zeros as $x=-3\ (multiplicity\ 2), 0,2$ or $\{-3\ (multiplicity\ 2), 0,2\}$
(b) For $f(x)\ge 0$, we can identify the intervals as $\{-3\}U[0,2]$
(c) For $f(x)\le 0$, we can identify the intervals as $(-\infty,0]U[2,\infty)$
