Answer
a. See graph
b. The $x$-intercepts are $(0,0)$ and $\left(\frac{5}{2},0\right)$.
c. The real zeros are $x=0$ and $x=\frac{5}{2}$.
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 $y=4x^3-20x^2+25x$ is as shown.
b. From the graph, the $x$-intercepts are $(0,0)$ and $\left(\frac{5}{2},0\right)$.
c.
Set $y=0$:
$$0=4x^3-20x^2+25x$$ $$0=x(4x^2-20x+25)$$ $$0=x(2x-5)^2$$ $$x=0$$ $$2x-5=0$$ $$x=\frac{5}{2}$$ Thus, the real zeros are $x=0$ and $x=\frac{5}{2}$.
d. The results from part (c) and those from part (b) are the same.
