Answer
a. See graph
b. The $x$-intercepts are $(-2,0)$, $(-1,0)$, $(0,0)$, $(1,0)$ and $(2,0)$.
c. The real zeros are $x=-2$, $x=-1$, $x=0$, $x=1$ and $x=2$.
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 $y=x^5-5x^3+4x$ is as shown.
b. From the graph, the $x$-intercepts are $(-2,0)$, $(-1,0)$, $(0,0)$, $(1,0)$ and $(2,0)$.
c.
Set $y=0$:
$$0=x^5-5x^3+4x$$ $$0=x(x^4-5x^2+4)$$ $$0=x(x^2-1)(x^2-4)$$ $$0=x(x+1)(x-1)(x+1)(x-2)$$ $$x_1=0$$ $$x+1=0$$ $$x_2=-1$$ $$x-1=0$$ $$x_3=1$$ $$x+2=0$$ $$x_4=-2$$ $$x-2=0$$ $$x_5=2$$
Thus, the real zeros are $x=-2$, $x=-1$, $x=0$, $x=1$ and $x=2$.
d. The results from part (c) and those from part (b) are the same.
