Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(0,0)$, $(1.5,0)$ and $(6,0)$.
(c) The solution is $x=0,1.5,6$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
Work Step by Step
(a) The graph is as shown.
(b) The $x$-intercepts are $(0,0)$, $(1.5,0)$ and $(6,0)$.
(c) Setting $y=0$:
$$0=2x^4-15x^3+18x^2$$
$$x^2(2x-3)(x-6)=0$$
$$x=0$$
$$2x-3=0$$
$$2x=3$$
$$x=\frac{3}{2}=1.5$$
$$x-6=0$$
$$x=6$$
Thus, the solution is $x=0,1.5,6$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
