AnswersSC-TX-TSIA2-Mathematics 26-27 Senior CourseSolving Polynomial Equations using Technology

Solving Polynomial Equations using Technology Answers

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1
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The polynomial equation has complex roots . What is the other root? Use a graphing calculator and a system of equations.

Question illustration
A
–3
B
–1
C
3
D
10
2
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Josh graphs a system of equations to determine the roots of the polynomial equation . From the graph, he determines that there are two solutions to the equation. Which statement is true?

Question illustration
A
He is correct because the graph shows two intersection points.
B
He is correct because the least exponent of the system is two so there must be two solutions.
C
He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be multiplicities or complex.
D
He is not correct because the difference of the exponents is three, so there must be three solutions, one of which is a multiplicity.
3

The aspect ratio is used when calculating the aerodynamic efficiency of the wing of a plane. For a standard wing area, the function can be used to find the aspect ratio depending on the wingspan in feet. If one glider has an aspect ratio of 5.7, which system of equations and solution can be used to represent the wingspan of the glider? Round solution to the nearest tenth if necessary.

Question illustration
A
and ; feet
Option A
B
and ; feet
Option B
C
and ; feet
Option C
D
and ; feet
Option D
4

The polynomial equation has complex roots . What are the other roots? Use a graphing calculator and a system of equations.

Question illustration
A
–64, 0
B
–2, 2
C
–1, 1
D
0, 64
5

Which system of equations can be used to find the roots of the equation ?

Question illustration
A
StartLayout Enlarged left-brace 1st Row y = 12 x cubed minus 5 x 2nd row y = 2 x squared + x + 6 EndLayout
Option A
B
StartLayout Enlarged left-brace 1st Row y = 12 x cubed minus 5 x + 6 2nd row y = 2 x squared + x EndLayout
Option B
C
StartLayout Enlarged left-brace 1st Row y = 12 x cubed + 2 x squared minus 4 x 2nd row y = 6 EndLayout
Option C
D
StartLayout Enlarged left-brace 1st Row y = 12 x cubed + 2 x squared minus 4 x + 6 2nd row y = 0 EndLayout
Option D
6

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.

Question illustration
A
–3, –5
B
–2.24, –2, 2.24
C
–2.24, 2, 2.24
D
3, 5
7

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–40, –4, 5
B
–5, 4, 40
C
–4, –1, 2
D
–2, 1, 4
8

Arlana graphed the system of equations that can be used to solve . What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.

Question illustration
A
–26, –9.81, 1.94
B
–26
C
–2
D
–2, 0.11, 4.39
9

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.

Question illustration
A
–12, 20
B
–2.73, 2, 2.73
C
–1.73, 1.73, 2
D
–20, 12
10

A parabolic listening device is shaped such that the depth of the bowl depends on its radius and can be represented by the curve D(r) = 0.145r2. What is the radius when the depth is 8 inches? Round to the nearest thousandth of an inch.

A
4.417 inches
B
5.252 inches
C
7.428 inches
D
20.505 inches

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