Answer
a. See graph
b. The $x$-intercepts are $(-3,0)$, $(0,0)$ and $(3,0)$.
c. The real zeros are $x=-3$, $x=0$ and $x=3$.
d. The results from part (c) and those from part (b) are the same.
Work Step by Step
a. Using a graphing utility, the graph of the function $y=\frac{1}{5}x^5-\frac{9}{5}x^3$ is as shown.
b. From the graph, the $x$-intercepts are $(-3,0)$, $(0,0)$ and $(3,0)$.
c.
Set $y=0$:
$$0=\frac{1}{5}x^5-\frac{9}{5}x^3$$ $$0=\frac{1}{5}x^3(x^2-9)$$ $$0=\frac{1}{5}x^3(x+3)(x-3)$$ $$x_1=0$$ $$x+3=0$$ $$x_2=-3$$ $$x-3=0$$ $$x_3=3$$ Thus, the real zeros are $x=-3$, $x=0$ and $x=3$.
d. The results from part (c) and those from part (b) are the same.
