AnswersINMT3 Integrated Math 3 Sem 1 26-27Solving 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 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
2
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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
3

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
4

Which equation can be solved by using this system of equations?

Question illustration
A
3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 = 0
Option A
B
3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 = 4 x Superscript 4 Baseline + 6 x cubed minus 11
Option B
C
3 x Superscript 5 Baseline + 4 x Superscript 4 Baseline + x cubed + 2 x squared minus 10 x minus 7 = 0
Option C
D
4 x Superscript 4 Baseline + 6 x cubed minus 11 = 0
Option D
5

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
6

The mass of a cylinder made of barium with a height of 2 inches depends on the radius of the cylinder as defined by the function . Which system of equations and solution can be used to represent the radius if the mass of the cylinder is 11,000 grams? Round to the nearest hundredth of an inch.

Question illustration
A
and ; inches
Option A
B
and ; inches
Option B
C
and ; inches
Option C
D
and ; inches
Option D
7

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
8

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.
9

The graph of this system of equations is used to solve . What represents the solution set?

Question illustration
A
y-intercepts of the graph
B
x-intercepts of the graph
C
y-coordinates of the intersection points
D
x-coordinates of the intersection points
10

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

Question illustration
A
StartLayout Enlarged left-brace 1st Row y = negative 4 x Superscript 5 Baseline + 12 x Superscript 4 Baseline minus 6 x 2nd row y = 5 x cubed minus 2 x EndLayout
Option A
B
StartLayout Enlarged left-brace 1st Row y = 4 x Superscript 5 Baseline minus 12 x Superscript 4 Baseline + 5 x cubed + 4 x 2nd row y = 0 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st row y = 4 x Superscript 5 Baseline minus 12 x Superscript 4 Baseline + 6x 2nd row y = negative 5 x cubed + 2 x EndLayout
Option C
D
StartLayout Enlarged left-brace 1st row y = 4 x Superscript 5 Baseline minus 12 x Superscript 4 Baseline + 6x 2nd row y = 5 x cubed minus 2 x EndLayout
Option D
11

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

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

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
13

The mass of a cylinder made of barium with a height of 2 inches depends on the radius of the cylinder as defined by the function . Which system of equations and solution can be used to represent the radius if the mass of the cylinder is 11,000 grams? Round to the nearest hundredth of an inch.

Question illustration
A
and ; inches
Option A
B
and ; inches
Option B
C
and ; inches
Option C
D
and ; inches
Option D
14

What is the root of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–3
B
0
C
2
D
3
15

Which equation can be solved by using this system of equations?

Question illustration
A
3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 = 0
Option A
B
3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 = 4 x Superscript 4 Baseline + 6 x cubed minus 11
Option B
C
3 x Superscript 5 Baseline + 4 x Superscript 4 Baseline + x cubed + 2 x squared minus 10 x minus 7 = 0
Option C
D
4 x Superscript 4 Baseline + 6 x cubed minus 11 = 0
Option D
16

Which equation can be solved by using this system of equations?

Question illustration
A
3 x cubed minus 7 x squared + 5 = 0
Option A
B
3 x cubed minus 7 x squared + 5 = 7 x Superscript 4 Baseline + 2 x
Option B
C
7 x Superscript 4 Baseline + 2 x = 0
Option C
D
7 x Superscript 4 Baseline + 3 x cubed minus 7 x squared + 2 x + 5 = 0
Option D
17

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation can be used to find x. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
The length is 7 inches, the width is 4 inches, and the height is 16 inches.
B
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
C
The length is 4 inches, the width is 1 inch, and the height is 13 inches.
D
The length is 3 inches, the width is 0 inches, and the height is 12 inches.

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