Answer
(a) $\{-\frac{5}{2},1, 3\ (multiplicity\ 2)\}$
(b) $(-\frac{5}{2},1)$
(c) $(-\infty,-\frac{5}{2})U(1,3)U(3,\infty)$
Work Step by Step
(a) Graph the function $f(x)=2x^4-9x^3-5x^2+57x-45$ as shown in the figure. We can identify the zeros as $x=-\frac{5}{2},1, 3\ (multiplicity\ 2)$ or $\{-\frac{5}{2},1, 3\ (multiplicity\ 2)\}$
(b) For $f(x)\lt 0$, we can identify the intervals as $(-\frac{5}{2},1)$
(c) For $f(x)\gt 0$, we can identify the intervals as $(-\infty,-\frac{5}{2})U(1,3)U(3,\infty)$
