Real Zeros of Polynomial Function...2

[nycmathguy]

Section 2.2
Question 48

For 48a, the zeros are x = -5, x = 4, and x = 5.

For 48b, at x = -5, the graph touches the x-axis forming odd multiplicity. At x = 4 and x = 5, the graph crosses the x-axis forming even multiplicity. NOTE: I am slightly confused about this multiplicity stuff.

For 48c, the graph is a 3rd degree polynomial. So, there are a maximum of 2 turning points.

For 48d, see below. Which one of the following graphs is more accurate for this type of question? I say the first one.

You say?

 

[MathLover1]

For 48a, the zeros are x = -5, x = 4, and x = 5.=> correct

For 48b, at x = -5, the graph touches =>incorrect
at x = -5, the graph crosses the x-axis and x = -5 has multiplicity 1
At x = 4 the graph crosses the x-axis and x = 4 has multiplicity 1
and
x = 5, the graph crosses the x-axis and x = 5 has multiplicity 1

means each root comes ones

For 48c => correct

 

[nycmathguy]

For 48a, the zeros are x = -5, x = 4, and x = 5.=> correct

For 48b, at x = -5, the graph touches =>incorrect
at x = -5, the graph crosses the x-axis and x = -5 has multiplicity 1
At x = 4 the graph crosses the x-axis and x = 4 has multiplicity 1
and
x = 5, the graph crosses the x-axis and x = 5 has multiplicity 1

means each root comes ones

For 48c => correct

Ok. I got 2 out 3 right. Not too bad. This multiplicity stuff is a bit confusing.