Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(-3,0)$, $(-1,0)$, $(1,0)$ and $(3,0)$.
(c) The solution is $x=-3,-1,1,3$.
(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 $(-3,0)$, $(-1,0)$, $(1,0)$ and $(3,0)$.
(c) Setting $y=0$:
$$0=x^4-10x^2+9$$
Let $u=x^2$:
$$0=u^2-10u+9$$
$$(u-1)(u-9)=0$$
$$u-1=0$$
$$u=1$$
Substitute back $u=x^2$:
$$x^2=1$$
$$x=\pm1$$
$$x_1=1$$
$$x_2=-1$$
$$u-9=0$$
$$u=9$$
Substitute back $u=x^2$:
$$x^2=9$$
$$x=\pm3$$
$$x_3=3$$
$$x_4=-3$$
Thus, the solution is $x=-3,-1,1,3$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
