Question 1038656: I'm not sure how to answer this problem:
find the real zeros of the given polynomial and their corresponding multiplicities.
Use this information along with a sign chart to provide a rough sketch of the graph of the
polynomial. Compare your answer with the result from a graphing utility.
a(x) = x(x + 2)^2
Please, please help, thank you!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In order for ) to be zero, either  has to be zero or  has to be zero. Since the factor is repeated twice (in other words, squared), the multiplicity of the zero  is 2.
Regardless of the value of , ^2\ >\ 0) . Hence the sign of is dependent on the sign of .
So, as gets large in the negative direction, also gets large in the negative direction. As gets large in the positive direction, gets large in the positive direction.
At zero, transitions from negative to positive going from left to right.
At -2, since the factor is squared, you approach zero from below, become tangent to the -axis at and then decreases again. Somewhere between -2 and 0, the function reverses direction again and starts to increase.
.jpg)
John
My calculator said it, I believe it, that settles it
|
|
|
