Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(-5,0)$, $(-2,0)$, $(2,0)$ and $(5,0)$.
(c) The solution is $x=-5,-2,2,5$.
(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 $(-5,0)$, $(-2,0)$, $(2,0)$ and $(5,0)$.
(c) Setting $y=0$:
$$0=x^4-29x^2+100$$
Let $u=x^2$:
$$0=u^2-29u+100$$
$$(u-25)(u-4)=0$$
$$u-25=0$$
$$u=25$$
Substitute back $u=x^2$:
$$x^2=25$$
$$x=\pm{5}$$
$$x_1=5$$
$$x_2=-5$$
$$u-4=0$$
$$u=4$$
Substitute back $u=x^2$:
$$x^2=4$$
$$x=\pm2$$
$$x_3=2$$
$$x_4=-2$$
Thus, the solution is $x=-5,-2,2,5$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
