Answer
(a) $\{-5\ (multiplicity\ 2), -\frac{3}{4}, 4\}$
(b) $(-\frac{3}{4},4)$
(c) $(-\infty,-5)U(-5,-\frac{3}{4})U(4,\infty)$
Work Step by Step
(a) Graph the function $f(x)=4x^4+27x^3-42x^2-445x-300$ as shown in the figure. We can identify the zeros as $x=-5\ (multiplicity\ 2), -\frac{3}{4}, 4$ or $\{-5\ (multiplicity\ 2), -\frac{3}{4}, 4\}$
(b) For $f(x)\lt 0$, we can identify the intervals as $(-\frac{3}{4},4)$
(c) For $f(x)\gt 0$, we can identify the intervals as $(-\infty,-5)U(-5,-\frac{3}{4})U(4,\infty)$
