Answer this for 100 points
2 answers:
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Answer:
Part 1)
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Part 2
The factored form is
Step-by-step explanation:
Part 1.
The missing diagram is shown in the attachment.
The zeroes of the seventh degree polynomial are the x-intercepts of the graph.
From the graph, we have x-intercepts at:
,
,
, and
.
The multiplicities tell us how many times a root repeats.
Also, even multiplicities will not cross their x-intercept, while odd multiplicities cross their x-intercepts.
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Note that the total multiplicity must equate the degree.
Part 2)
According to the factor theorem, if is a zero of p(x), then
is a factor.
Using the multiplicities , we can write the factors as:
Therefore the completely factored form of this seventh degree polynomial is
Slope = (y2 - y1)/(x2 - x1) = (1 - 3)/(-2 - (-5)) = -2/(-2 + 5) = -2/3
For perpendicular lines, m2 = -1/m1 = -1/(3/8) = -8/3
A line passing through point (-4, 0) and parallel to the y-axis is x = -4
radius = diameter/2 = 10/2 = 5
center of circle = midpoint of diameter = ((-3 + 5)/2, (1 + 7)/2) = (2/2, 8/2) = (1, 4)
Required equation is (x - 1)^2 + (y - 4)^2 = 5^2
(x - 1)^2 + (y - 4)^2 = 25
For perpendicular lines, m2 = -1/m1 = -1/(3/8) = -8/3
A line passing through point (-4, 0) and parallel to the y-axis is x = -4
radius = diameter/2 = 10/2 = 5
center of circle = midpoint of diameter = ((-3 + 5)/2, (1 + 7)/2) = (2/2, 8/2) = (1, 4)
Required equation is (x - 1)^2 + (y - 4)^2 = 5^2
(x - 1)^2 + (y - 4)^2 = 25