Using the Fundamental Theorem of Algebra. Complete the following exercises. Show your work.
Determine how many, what type, and find the roots for f(x) = x^4 + 21x^2 − 100.


Determine how many, what type, and find the roots for f(x) = x^3 − 5x^2 − 25x + 125.

Answers

Answer 1

Answer:

A) - Quartic polynomial

- has four roots

- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) - Cubic polynomial

- has 3 roots

- roots are; f(x) = (x - 5)²(x + 5)

Step-by-step explanation:

A) f(x) = x⁴ + 21x² − 100

The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.

Factorizing this polynomial gives;

f(x) = (x² + 25)(x² - 4)

Equating to zero, we can find the roots. Thus, the roots are;

x = 5i

x = -5i

x = 2

x = -2

Thus, the completely factorized polynomial is;

f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) f(x) = x³ − 5x² − 25x + 125

The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.

Factorizing this polynomial gives;

f(x) = (x² - 25)(x - 5)

Equating to zero and Factorizing gives;

x = 5

x = -5

x = 5

Thus, completely factorized with the roots is;

f(x) = (x - 5)²(x + 5)


Related Questions

help what's 1x1+9x20​

Answers

Answer:

The answer is 181

Step-by-step explanation:

PEDMAS

1 x 1 + 9 x 20

1 x 1 = 1

1 + 9 x 20

9 x 20= 180

1+180

which equals 181

Answer:

181

Step-by-step explanation:1x1=1 9x20=180+1=181

Thats your answer my fellow brains

Solve the proportion then around your answer to the nearest hundredth

Answers

Answer:

[tex] \frac{6.3}{x} = \frac{2.56}{9.3} \\ x = \frac{6.3 \times 9.3}{2.56} \\ x = 22.89[/tex]

Answer:

x = 22.89

Step-by-step explanation:

6.3 / x = 2.56 / 9.3

Cross multiply

58.59 = 2.56x

Divide both sides by 2.56

22.88671875 = x

Round

x = 22.89

-2c + 8 - 7c - 6 -5c + 14 -5c + 14 -9c + 2 -9c + 2 9c - 14 9c - 14 5c + 14 5c + 14

Answers

Answer:

= -152c + 32

Step-by-step explanation:

sry if wrong

If P = (5,4), find the image
of P under the following rotation.
180° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.

Answers

Answer:

[tex](-5,-4)[/tex]

Step-by-step explanation:

Given

[tex]P = (5,4)[/tex]

Rotation: 180 degrees counterclockwise

Required

P'

Rotation: 180 degrees counterclockwise

The rule is:

[tex](x,y) \to (-x,-y)[/tex]

So: [tex]P = (5,4)[/tex] becomes

[tex](5,4) \to (-5,-4)[/tex]

What is Limit of g (x) as x approaches 1, if it exists?
0
7,000,000
700,000,000
DNE

Answers

Answer:

7,000,000

Step-by-step explanation:

Limit of a function:

The limit of a function is finding looking at it's lateral limits.

If the lateral limits are equal:

The limit exists.

[tex]\lim_{x \rightarrow a} f(x) = \lim_{x \rightarrow a^{+}} f(x) = \lim_{x \rightarrow a^{-}} f(x)[/tex]

If lateral limits are different:

That is:

[tex]\lim_{x \rightarrow a^{+}} f(x) \neq \lim_{x \rightarrow a^{-}} f(x)[/tex], then the limit does not exist.

In this question:

To the left of 1, that is, 0.9999....

[tex]\lim_{x \rightarrow 1^{-}} g(x) = 7,000,000[/tex]

To the right of 1, that is, 1.0001...

[tex]\lim_{x \rightarrow 1^{+}} g(x) = 7,000,000[/tex]

Since the both limits are the same, the limits exists and it's value is of  7,000,000.

Answer:

D

Step-by-step explanation:

It shows it in the quwestions image

I don’t understand how to solve this. Please explain the steps. Thanks.

Answers

Answer:

D

Step-by-step explanation:

When you are raising something to a fractional power, you are raising it to the power of the numerator and finding the root denoted by the denominator. The explanation above is kinda confusing, so here is an example:

x^(3/5)

This would be written as:

[tex]\sqrt[5]{x^3}[/tex]

Now for the actual problem. Since the numerator is 4, we start by raising x to the 4th power, x^4.

Because the denominator is 5, we find the 5th root:

[tex]\sqrt[5]{x^4}[/tex]

This matches none of the answers shown, so the answer is none of the above or D.

Answer:

D

Step-by-step explanation:

The answer would be 5 square root x^4

See Image Below:)

The population of Nowhere, USA was estimated to be 665,200 in 2004, with an expected increase of 1.9 % per year. At the percent of increase
given what was the expected population in 2005? Round your answer to the nearest whole number.

Answers

Answer:

677838 people

Step-by-step explanation:

1.9 percent of 665200 is 12638

665200+12638=677838

HELP! can anyone help? I’m pretty stuck and the answer isn’t 2,700.. I’ll give Brainly please :(

Answers

Answer: $2603.90

Step by step solution: See photo

4
3
3
2+
-4
-3
-2 -1
1
1
2
3
4
-1+
-2+
-3
-4
What is the slope of the line?

Answers

Answer:

2/3

Step-by-step explanation:

rises 2 units and east 3 units

rise / run = 2 / 3

8

4

A gold bar is similar in shape to a rectangular prism. A gold bar is

7 1

approximately 7 in.x3 in.x1 in. If the value of gold is $1,214 per ounce,

about how much is one gold bar worth? Use the formula w 11.15n, where w

is the weight in ounces and n=volume in cubic inches, to find the weight in

ounces. Explain how you found your answer.

Answers

Answer:

[tex]Worth = \$284258.1[/tex]

Step-by-step explanation:

Given

[tex]Dimension: 7in\ * 3in\ * 1in[/tex]

[tex]Value = \$1214/oz[/tex] ---- value of Gold

Required

The worth of 1 gold bar

First, calculate the volume (n) of the gold bar

[tex]n = 7in * 3in * 1in[/tex]

[tex]n = 21in^3[/tex]

Next, calculate the weight of the gold bar using:

[tex]w = 11.15n[/tex]

[tex]w = 11.15 * 21[/tex]

[tex]w = 234.15oz[/tex]

Multiply the value of Gold by the weight of the gold bar to get the worth of the gold bar.

[tex]Worth =Value * w[/tex]

This gives:

[tex]Worth = \$1214/oz * 234.15oz[/tex]

[tex]Worth = \$1214 * 234.15[/tex]

[tex]Worth = \$284258.1[/tex]

please help with this math question

Answers

263.27 m^2

rectangle : 15 x 10 = 150 m^2
the half circle at the top has a diameter of 6m. therefore, it’s radius is 3m. if it is cut in half, the part removed from the triangle height is 3m. therefore, the height of the triangle is 35 -15 = 20; 20 - 3 = 17. the height of the triangle is 17. the triangle area formula is a = 1/2(bh).
a = 1/2 (10)(17)
a = 1/2 (170)
a = 85 m^2
the circle would be a = πr^2 but divided by 2 bc it’s a half circle
a = π(3)^2
a = π9
a = 28.27 m^2
150 + 85 + 28.27 = 263.27 m^2

UYK
♡ The size of a rhombus is half the longer diagonal.
The height of the ronbus is 3cm
and
the area is 21cm². Find the length of the longer
diagonal

Answers

Answer:

Step-by-step explanation:

Area = height × side

 

21   = 3 * side

 

side = 7 cm

The side of a rhombus is half the longer diagonal

longer diagonal = 2*side =2*7=14cm

5 gal- 1 qt = _____ gal ______ qt

Answers

4 gallons (gal) & 0 quarts (qt)

Q8. How many solutions does the system of equations have?

Answers

Answer:

it would be the first answer

Step-by-step explanation:

a solution is where the lines meet, and the coorinate is (1,4)

the answer would b A !

Math grade 9, can anyone solve it

Answers

Answer:

a) Acceleration = 2.4 m per seconds²

b) Distance traveled = 132 m

Step-by-step explanation:

a). Acceleration of an object is defined by the equation,

v = u + at

Here, v = Final speed

u = Initial speed

a = Acceleration

t = Duration Or time

From the graph attached,

Between t = 0 and t = 5 seconds,

v = 12 meter per second

u = 0

t = 5 seconds

B substituting values in the equation,

12 = 0 + a(5)

a = [tex]\frac{12}{5}[/tex]

a = 2.4 m per seconds²

b). Equation representing distance traveled by an object,

v² = u² + 2as

Here, v = Final speed

u = Initial speed

a = Acceleration

s = Distance traveled

By substituting these values in the given equation,

1). Between t = 0 to t = 5 seconds,

(12)² = 0 + 2(2.4)s

s = [tex]\frac{144}{4.8}[/tex]

s = 30 m

2). Between t = 5 to t = 12 sec

Car moved with a constant speed (Acceleration = 0)

Distance traveled = Speed × Time

                             = 12 × 7

                             = 84 m

3). Acceleration of the car between t = 12 sec to t = 15 sec

By substituting the values in the equation,

v = u - at

0 = 12 - a(3)

a = 4 meter per seconds²

Distance traveled in this duration,

v² = u² - 2as

0 = (12)² - 2(4)s

144 = 8s

s = [tex]\frac{144}{8}[/tex]

s = 18 m

Therefore, total distance covered by the car = 30 + 84 + 18

= 132 meters


Which graph represents the equation y=-
--*x+3?
B)
t

Answers

Answer:

The correct answer would be the 3rd graph!

Hope this helps!

I'm a bit confused about this, can anyone help? Giving 69 points to whoever answers by 12:30 PM (PST)!!

Find the area of the polygon:

Answers

Answer: i can give you tips of how to find the area of a polygon.

OK SO To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides.

Step-by-step explanation:

And you have to add all the sides of the lengths of the sum of the polygon


Use Pythagorean Theorem to determine if the three
given sides create a right triangle.
15 m, 8 m, 17 m
Show your work

Answers

Answer:

Yes, it is a right triangle.

Step-by-step explanation:

8²+15²=17²

64+225=289

289=289 YES, it is a right triangle

Find the product of
(−9−11i) and its conjugate.

Answers

Answer:

202

Step-by-step explanation:

First, we can find the conjugate of (-9 -11i)

Given a complex number a + bi, the conjugate would be a - bi.

So, the conjugate of -9 -11i is -9 + 11i.

Now, we multiply!

(-9-11i)(-9+11i)

This resembles the special product (a+b)(a-b) which multiplies out to a^2 - b^2

To apply this we subtract the square of the second number from the first.

(-9)^2 - (11i)^2

81 - 121i^2

i^2 is -1, so we can substitute it in:

81 + 121 = 202

What coordinates will remain the same? What coordinates will change to the opposite between the pre-- and post-image?

Answers

Answer:

Y values will stay the same

Step-by-step explanation:

Reflecting over the Y axis will alter the distance left and right but not up and down. so only Y remains unchanged


Indra completed 85% of a Multiple Choice Test in Science. She has 3
questions to complete.
(a) How many questions are there in the test?

Answers

Answer:

20 questions

Step-by-step explanation:

There is 15% of the test left and 3 questions

15/3 = 5

85/5 = 17

17+ 3 = 20

NO LINKS!!!! Find each measurement indicated. Round your answer to the nearest tenth. Part 2c​

Answers

9514 1404 393

Answer:

BC = 24.0AC = 26.0m∠B = 73.4°m∠B = 30.0°

Step-by-step explanation:

The law of sines tells you the ratio of sides is the same as the ratio of sines of their opposite angles.

This post has 2 kinds of problems.

1) 2 angles and the side between them are given.

2) 2 sides and the angle opposite the longest is given.

For the first type, you need to determine the missing angle (opposite the given side). That comes from the sum of angles of a triangle being 180°. Then you find the remaining sides using the ratio of sines.

For the second type, the angle opposite the shorter side is found using the ratio of sides to find the sine of that angle. Then the third side and third angle can be found using the ratio of sides to find the sine of the angle, and using the ratio of sines to find the missing side.

Straightforward, and tedious. For more than one, I like to use a spreadsheet to crunch the numbers.

_____

1) BC = 24.0

2) AC = 26.0

3) m∠B = 73.4°

4) m∠B = 30.0°

__

In the spreadsheet, the given values are in the first 3 columns. The 4th column is the first one calculated. As indicated above, the angle calculation for problems 1 and 2 uses the sum of angles relation. For problems 1 and 2, this is the angle opposite the given side. The "first side" is the side opposite the "first angle". c = b·sin(C)/sin(B), for example.

For problems 3 and 4, the first unknown angle is the one opposite the "short side", which is the shorter of the given sides. As it happens, this is the side that is asked for in the question. B = arcsin(c·sin(B)/sin(C))

_____

Additional comment

In a spreadsheet, angles are presumed to be in radians for all of the trig functions. We use the DEGREES( ) and RADIANS( ) functions to convert as appropriate.

a length of 25 meters.cindy cut the string in 4 pieces of equal length.how was each piece​

Answers

Answer:

6.25 meters

Step-by-step explanation:

25/4 = 6.25

Length of each cut piece is 6.25 m.

What is division?

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given

A length of 25 meters cut the string in 4 pieces of equal length.

= [tex]\frac{25}{4}[/tex]

= 6.25

Length of each cut piece is 6.25 m.

Find more information about division here

https://brainly.com/question/5805897

#SPJ2

A film on TV starts at 8:30 pm. If the film takes 136 minutes, at
what time does it end?

Answers

Answer:

10:46

Step-by-step explanation:

8:30 + 136 min.

= 8:30 + 2:16

= 10:46

What ratio/s are equivalent to the following ratio: 6:8
a 3:4 b 12:16. с 18:24 d 30:40​

Answers

Answer:

a. 3/4

Step-by-step explanation:

6:8

=6/8

=3/4

Hope it Helps

Find the length of missing side BC and AC.


Best answer gets brainliest!!!

Answers

Answer:

b = 7.56

C = 9.24

Step-by-step explanation:

Find the last angle of the triangle.

The sum of all the angles in a triangle is  

180 degrees.

A+

90+55=180

A=35

Then find c

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(B)=adj/hyp or Cos(55) = 5.3 / c

re write as

C = 5.3 / cos55

This gives you c = 9.24

Then use the Pythagorean theorem to find the unknown side.

[tex]a^{2} +b^{2} = c^{2} \\rewrite as\\ b^{2} = c^{2} - a^{2} \\b^{2} = 9.2^{2} - 5.3^{2} \\b^{2} = 57.29\\b = 7.56[/tex]

Help with this question!Please

Answers

Answer:

x = 14 for the first one, x = 60 for the second one

Step-by-step explanation:

Step-by-step explanation:

We know the measure of a straight line is 180° . So that ,

> 5x - 10 + 120 = 180

> 5x = 60 + 10

> 5x = 70

> x = 70/5

> x = 14

Solution 2 :-

> x + 50 + 70 = 180

> x = 180 - 120

> x = 60

what is matter and it function​

Answers

Answer:

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume.

Step-by-step explanation:

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume.

A dry cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 15 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject thenull hypothesis that p= 0.7; otherwise, we conclude that p > 0.7.

Required:
a. Evaluate α, assuming that p = 0 .7.
b. Evaluate β for the alternative p = 0.9.

Answers

Answer:

α = 1 - 0,915 = 0.085

β = 0.314

Step-by-step explanation:

Dry cleasning clain that spot remover will remove the 70% of spot. The claim support the spot and chose at random.

Null hypothesis:

H0 : p = 0.7

If 11 of spot are removed then hypothesis rejected.

If 11 spots are not removed then hypothesis accepted

H1 : p >0/7

X is the number of spot and binomial random variable.

For a)

The probability of committing the type 1 error use alpha such as

α = P ( type I error)

where X > 10

and p = 0.7

for the given values where n = 12 and r = 10 and p - 0.7

we get

α = 1 - 0,915 = 0.085

b)

The nonrejection of the hypothesis where type II error is false .

The hypothesis for this is 0.9

This is Type II error

β = P ( type II error) = P ( X <= 10 where p = 0.9 )

Where n = 12 , r = 10 and p = 0.9

then

β = 0.314

What is the length of AC?

Answers

The length of AC 90°
Other Questions
Edexcel exam due date on may June 2021? On which date is it starting Find all vertical asymptotes of the following function f(x)=9x^2-64/2x+14 Exercise 1: Identifying Verbals- In the following sentences, first identify the verbal, then what kind of verbal (gerund, present participle, past participle or infinitive) is present in the sentence. Then write its function in the sentence (noun, adjective, or adverb). 1. Samantha left the movie early to eat dinner with her family.Verbal: Type of Verbal:Function of Verbal: A large Map scale shows ___________ ?A . a large area with little information.B. a small area with little information.C. New York State.D. a smaller area with more details and information like the names of streets. How can cooperation become fun? Find the surface area of the rectangular prism A balloon can be inflated with 4.23 Liters of O2gas at STP. How much will the balloon weigh in grams? Which ingredient helps add texture and volume to food? Name the three labeled segments that are parallel to EF Why does Africa's climate have a striped (or zonal) pattern?OmeridiansO longitudeO latitudeO rainfall HELP ASAP!!!!!!!!!!Please PLssssssssssssssssssssss help. Write the expression 53.7124 x 10 x 3 as a single number. Use the distributive property to expand - 3x * (4d - 5e - 3f) Anyone got me ? Let me knowww :) The file format is used for graphic files. What is the product? StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFractionStartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFractionStartFraction x (x minus 1) Over 2 EndFractionStartFraction (x + 4) (x minus 4) Over 2 x (x minus 1) EndFractionStartFraction (x minus 4) (x minus 1) Over 2 x (x + 4) EndFraction 3 (x-1) - 8 = 4 (1+x) + 5 Solve it please? HELP PLEASE The gift shop at a science museum sells lollipops that are made to look like the planets. Each lollipop is shaped like a sphere and has a radius of 121212 mm.What is the volume of each lollipop?Either enter an exact answer in terms of \pipi or use 3.143.143, point, 14 for \pipi. What is the scale factor?