Zero of 7 with a multiplicity of 3 means one factor is
Zero of -1 with a multiplicity of 2 means one factor is
Zero of 5 with a multiplicity of 1 means one factor is
Multiplying, we get
That's already in factored form so we leave it here.
I need help understanding complex zeros of a polynomial function. I've taken notes, I've watched videos, nothing helps. I'm lost
1 answer:
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To get you answer multiply the length and width twice. Then the length and height twice. Then the width and height twice. And add it all up.
7* 1.25= 8.75
7* 1.25= 8.75
7*6.5= 45.5
7*6.5= 45.5
6.5*1.25=8.125
6.5*1.25=8.125
7* 1.25= 8.75
7* 1.25= 8.75
7*6.5= 45.5
7*6.5= 45.5
6.5*1.25=8.125
6.5*1.25=8.125
<h3>Answer: 80 degrees</h3>
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Explanation:
I'm assuming that segments AD and CD are tangents to the circle.
We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.
By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.
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Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.
Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.
We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.
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Here's what we have so far for quadrilateral DAEC
- angle A = 90
- angle E = 100
- angle C = 90
- angle D = unknown
Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees
A+E+C+D = 360
90+100+90+D = 360
D+280 = 360
D = 360-280
D = 80
Or a shortcut you can take is to realize that angles E and D are supplementary
E+D = 180
100+D = 180
D = 180-100
D = 80
This only works if AD and CD are tangents.
Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.