AnswersINMT3 Integrated Math 3 Sem 1 26-27Solving Polynomial Equations using Technology

Solving Polynomial Equations using Technology Answers

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The following system of equations can be used to find the roots of the equation x3 + 72 = 5x2 + 18x.y = x3 + 72y = 5x2 + 18xGraph this system of equations on the graphing calculator.How many intersection points can you see in the default viewing window? ✔ 123

A
✔ 1
B
2
C
3
2
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Adjust the window so you can find all of the points of intersection for the system of equations.What are the roots of the original polynomial equation? Check all that apply.

A
–6
B
0
C
6
D
–4
E
3
F
8
3

Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?

A
y = 2x3 + x2 + 3x +5y =9
B
y = 2x3 + x2 y = 3x + 14
C
y = 2x3 + 4x2 – x + 5 y = –3x2 + 4x + 9
4

From least to greatest, what are the roots of the polynomial equation?

Answers:
Blank 1:-4
Blank 2:-0.5
Blank 3:1
5

Question text not available

Answer:

-0.5

6

Question text not available

Answer:

1

7

Use a graphing calculator and a system of equations to find the roots of the equation. x4 − 4x3 = 6x2 − 12x From least to greatest, what are the integral roots of the equation? and

Answer:

-2

8

What are the approximate values of the non-integral roots of the polynomial equation?

A
–5.57
B
–1.95
C
0.21
D
1.27
E
4.73
9

Question text not available

Answer:

0

10

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form an open box. The volume of the box is 420 in.3.The equation 4x3 – 72x2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.What is the side length of the square that is cut from each corner, to the nearest inch? in.

Answer:

3

11

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Answer:

A graphing calculator shows real-valued graphs in the Cartesian plane, so it can find or approximate real solutions shown as x-intercepts. Some polynomial equations also have complex solutions, which cannot be represented as x-intercepts on that graph. Thus, graphing cannot find or approximate all polynomial solutions.

12

Did your explanation include the following?

A
Some polynomial equations have complex solutions.
B
Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.
C
Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.
13

Compare the two methods that you learned for finding or approximating solutions to polynomial equations. What are the pros and/or cons of each? Explain.

Answer:

Factoring can give exact solutions when a polynomial factors easily, but finding the factors can be difficult. Graphing is useful for estimating real solutions when factoring is difficult, but the answers may be approximate, and a graph does not show complex solutions.

14

Select any of the following you included in your explanation.

A
Graphing the related system means that you do not have to rewrite the equation to set it equal to 0. It is easier because you can just graph each side of the equation.
B
Sometimes it is difficult to locate the intersection point for the system. You might have to zoom in a lot or figure out how to resize the window. Using the related function lets you focus on the x-axis to find the points.
15

Sun shades are sold in the shape of right isosceles triangles. If the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?

Question illustration
A
[image 1] and [image 2]
Option A
B
[image 1] and [image 2]
Option B
C
[image 1] and [image 2]
Option C
16

Question text not available

Answers:
Use the graphing calculator to graph the system. The solutions to the system are . Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet.:-11.3 or 11.3
Use the graphing calculator to graph the system. The solutions to the system are . Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet.:11.3
17

-5.7 or 5.7-8 or 8✔ -11.3 or 11.3-32 or 32

Answers:
Use the graphing calculator to graph the system. The solutions to the system are . Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet.:-11.3 or 11.3
Use the graphing calculator to graph the system. The solutions to the system are . Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet.:11.3
18

5.78✔ 11.332

A
5.7
B
8
C
✔ 11.3
D
32

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