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tia_tia [17]
2 years ago
12

The polynomial equation x^6-16x^2=4x^4-64 has complex roots +- 2i . What are the other roots? Use a graphing calculator and a sy

stem of equations.
Mathematics
2 answers:
Gekata [30.6K]2 years ago
6 0

option B

which is roots are -2 and 2


Irina18 [472]2 years ago
3 0
Use u subsitution the solve by grouping
u=x^2
u^3-16u=4u^2-64
u^3-4u^2-16u+64=0
(u^3-4u^2)+(-16u+64)=0
u^2(u-4)+(-16)(u-4)=0
(u^2-16)(u-4)=0
(u-4)(u+4)(u-4)=0
(u+4)(u-4)^2=0

u=x^2
(x^2+4)(x^2-4)^2=0
(x^2+4)((x-2)(x+2))^2=0
(x^2+4)(x-2)²(x+2)²=0
set to zero

x^2+4=0
x^2=-4
x=+/-2i

x-2=0
x=2

x+2=0
x=-2

the other roots are -2 and 2

for graphinc calculator, graph and find x intercepts
You might be interested in
Please answer I will give brainiest. 24 is (8 1/3) percent of what number? I know how to do it but the SMALL decimal I am gettin
Liono4ka [1.6K]

Answer:

288

Step-by-step explanation:

24 = 8 1/3 % of x

24 = (25/3 * 1/100)x

25/300 x = 24

x = 24 * 300/25

x = 7200/25

x = 288

5 0
3 years ago
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an a
Scrat [10]

Answer:

The answer is (C) 8

Step-by-step explanation:

First, let's calculate the length of the side of the square.

A_{square}=a^2, where a is the length of the side. Now, let's try to build the square. First we need to find a point which distance from (0, 0) is 10. For this, we can use the distance formula in the plane:

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} which for x_1=0 and y_1 = 0 transforms as  d=\sqrt{(x_2)^2 + (y_2)^2}. The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, x_2, y_2 and 10 are a Pythagorean triple. From this, x_2= 6 or  x_2=8 while y_2= 6 or y_2=8. This leads us with the set of coordinates:

(\pm 6, \pm 8) and (\pm 8, \pm 6).  (A)

The next step is to find the coordinates of points that lie on lines which are perpendicular to the lines that joins the origin of the coordinate system with the set of points given in (A):

Let's do this for the point (6, 8).

The equation of the line that join the point (6, 8) with the origin (0, 0) has the equation y = mx +n, however, we only need to find its slope in order to find a perpendicular line to it. Thus,

m = \frac{y_2-y_1}{x_2-x_1} \\m =  \frac{8-0}{6-0} \\m = 8/6

Then, a perpendicular line has an slope m_{\bot} = -\frac{1}{m} = -\frac{6}{8} (perpendicularity condition of two lines). With the equation of the slope of the perpendicular line and the given point (6, 8), together with the equation of the distance we can form a system of equations to find the coordinates of two points that lie on this perpendicular line.

m_{\bot}=\frac{6}{8} = \frac{8-y}{6-x}\\ 6(6-x)+8(8-y)=0  (1)

d^2 = \sqrt{(y_o-y)^2+(x_o-x)^2} \\(10)^2=\sqrt{(8-y)^2+(6-x)^2}\\100 = \sqrt{(8-y)^2+(6-x)^2}   (2)

This system has solutions in the coordinates (-2, 14) and (14, 2). Until here, we have three vertices of the square. Let's now find the fourth one in the same way we found the third one using the point (14,2). A line perpendicular to the line that joins the point (6, 8) and (14, 2) has an slope m = 8/6 based on the perpendicularity condition. Thus, we can form the system:

\frac{8}{6} =\frac{2-y}{14-x} \\8(14-x) - 6(2-y) = 0  (1)

100 = \sqrt{(14-x)^2+(2-y)^2}  (2)

with solution the coordinates (8, -6) and (20, 10). If you draw a line joining the coordinates (0, 0), (6, 8), (14, 2) and (8, -6) you will get one of the squares that fulfill the conditions of the problem. By repeating this process with the coordinates in (A), the following squares are found:

  • (0, 0), (6, 8), (14, 2), (8, -6)
  • (0, 0), (8, 6), (14, -2), (6, -8)
  • (0, 0), (-6, 8), (-14, 2), (-8, -6)
  • (0, 0), (-8, 6), (-14, -2), (-6, -8)

Now, notice that the equation of distance between the two points separated a distance of 10 has the trivial solution (\pm10, 0) and  (0, \pm10). By combining this points we get the following squares:

  • (0, 0), (10, 0), (10, 10), (0, 10)
  • (0, 0), (0, 10), (-10, 10), (-10, 0)
  • (0, 0), (-10, 0), (-10, -10), (0, -10)
  • (0, 0), (0, -10), (-10, -10), (10, 0)

See the attached second attached figure. Therefore, 8 squares can be drawn  

8 0
2 years ago
Enter a number in the field below to show rewriting the division as multiplication. 3 4 ÷ 5 12 = 3 4 ×
Alexxandr [17]

Answer:

0.001953125

Step-by-step explanation:

Divide 34 by 512

34 ÷ 512 = 0.06640625

divide 0.06640625 by 34

0.06640625 ÷ 34 = 0.001953125

Check you work

34 × 0.001953125 = 0.06640625

Answer is 3 4 ÷ 5 12 = 3 4 × 0.001953125

4 0
3 years ago
Read 2 more answers
A linear function includes the ordered pairs (0, 1), (3, 3), and (9, n). What is the value of n?
alexgriva [62]
The answer is A I think
8 0
3 years ago
HELP! GIVING BRAINLIEST IF ANSWERED CORRECTLY AND FOR EACH SECTION!!!
Anon25 [30]

Answer:

[14] 139

[15] 90

[16] 41

[17] 49

[18] 139

[19] 131

Step-by-step explanation:

[14] Since m ∠ CEB is vertical with m ∠ AED = 139

[15] Knowing that m ∠FBD = 90 degree then m ∠ CEF = 90 degree

[16] Since m ∠ DEB is vertical to m ∠ADC Thus answer = 41

Note: vertical angles are angles opposite each other where two lines cross.

[17] Since m ∠ FED = 90 degree and m ∠ DEB = 41 then 90 - 41 = 49

[18] To Find m ∠CEB we have to subtract from m ∠ DEB

180 - 41 = 139

[19] Knowing that m ∠ FED = 90 degree and m ∠DEB = 41

Then m ∠ AEF =  90 +41=131

<u><em>~Lenvy~</em></u>

4 0
2 years ago
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