The polynomial of degree 4, P ( x ) , has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x = − 2 . It goes through the point ( 5 , 336 ) . Find a formula for P ( x ) . P ( x ) =___
Show your work

Answers

Answer 1

We want to find a polynomial given that we know its roots and a point on the graph.

We will find the polynomial:

p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x

We know that for a polynomial with roots {x₁, x₂, ..., xₙ} and a leading coefficient a, we can write the polynomial equation as:

p(x) = a*(x - x₁)*(x - x₂)...*(x - xₙ)

Here we know that the roots are:

x = 1 (two times)x = 0x = -2

Then the roots are: {1, 1, 0, -2}

We can write the polynomial as:

p(x) = a*(x - 1)*(x - 1)(x - 0)*(x - (-2))

p(x) = a*(x - 1)*(x - 1)*(x + 2)*x

We also know that this polynomial goes through the point (5, 336).

This means that:

p(5) = 336

Then we can solve:

336 = a*(5 - 1)*(5 - 1)*(5 + 2)*5

336 = a*(4)*(4)*(7)*5

336 = a*560

366/560 = a = 183/280

Then the polynomial is:

p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x

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Related Questions

Sarah's grandmother has a square blanket that covers an area of 25 square feet. Sarah wants to put a string of pearls around the sides of the blanket. How many feet long will the string of pearls have to be for Sarah to complete the job?

Answers

Answer:

20 ft

Step-by-step explanation:

area of square = (side)^2

area of square = 25 ft^2

(side)^2 = 25 ft^2

side = 5 ft since (5 ft)^2 = 25 ft^2

The side of the square measures 5 ft.

All around the square is the perimeter.

perimeter = 4 * side

perimeter = 4 * 5 ft

perimeter = 20 ft

Answer: 20 ft

-2 as a decimal
Help if you can ik it’s simple I’m just very tired :)

Answers

Not way to keen on it but it might be -0.02

Hope it helps!
2%= 0.02.. and changing it to a negative would be -0.02!

I hope this helps! & Let me know if you have any questions!

Mark this as Brainliest if you get a chance:)

NEED HELP FOR REAL 69 points!!!!!!!!!!!!!! ASAP
The physicist from the last problem lets the particle fall another 100 times, and finds that the average travel time is now 16 sec. Remember that when running the simulation many times it took 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. What does she conclude and why?

Answers

It concludes that newtons laws of motion are at work


Martina runs 3 miles in 25 minutes. At the same rate, how many miles would she run in 20 minutes?

Answers

Answer:

2 and a half mile

Step-by-step explanation:

As she runs three miles in 25 minutes so she can run 2 and a half miles in 20 minutes because she needs five minutes to complete the third mile

2 1/2 Miles in 20 minutes. I hope
this helps!

Ey pls help me anyone pls

Answers

Answer:

we cant read the whole question so I cant help you.

Step-by-step explanation:

Answer:

I will do 1-4 and explain because I dont have the time to do all of this.

1=130 2=130 3=134? 4=63 Just add up the numbers and subtract them from either 90 180 or 360, how to know which number to add up to is easy, just see if the sum of the numbers added makes a number above one of those numbers, for example if you find one that the sum is larger then 90 but smaller then 180 then subtract the sum from 180.

Step-by-step explanation:

Can anyone help me with this?

Answers

it does not show the question

An election is over and a new student body president has been elected. The new president received 3 votes for every vote received by his opponent. The new president received 2193 votes. How many votes did his opponent receive?

Answers

731 votes. Explanation: if his votes are 3:1 of his opponent’s votes. Divide 2193 by 3 to get 731 votes

can someone plz help me with this

Answers

Answer:

option D .....11

Option c 36

A+B + C = 180
A= 36
What is x

Answers

Answer:

which is x here

please write complete question


A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.12 for each minute of calls. Plan B costs $15 plus an additional $0.10 for
each minute of calls.
For what amount of calling do the two plans cost the
Same?

Answers

Answer:

250 minutes

Step-by-step explanation:

10 + 0.12x = 15 + 0.10x

0.02x + 10 = 15

0.02x = 5

x = 250

Your welcome!

Kayden Kohl

8th Grade Student

9% out of 432 kids want to be lawyers. How many kids did not want to be lawyers?

Answers

Answer:

393.12 kids. This is technically impossible, as you can't have 0.12 of a kid, so I will round down to 393 kids.

Step-by-step explanation:

9% = 0.09

x = amount of kids who want to be lawyers

y = amount of kids who do not want to be lawyers

x = 0.09(432)

x = 38.88

y = 432 - 38.88

y =  393.12

Right triangle CDE has its right angle at vertex
D. The length of DE is 8 feet and the length of
CE is 17 feet. What is the length, in feet, of CD?
A) 11
B) 12
C) 14
D) 15

Answers

The answer is A 11 feet

The length of the side CD which is the base of the right triangle CDE is 15 feet which is option D.

We have,

We can use the Pythagorean theorem to solve for the length of the height CD in the right triangle CDE.

Where CE is the hypotenuse and De is the base.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we have:

CD² + DE² = CE²

Plugging in the given lengths:

CD² + 8² = 17²

CD² + 64 = 289

CD² = 289 - 64

CD² = 225

CD = √225

CD = √15²

CD = 15

Thus,

The length of the side CD which is the base of the right triangle CDE is D. 15 feet.

Learn more about the Pythagorean theorem here:

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#SPJ3

If f(1) = 160 and

f(n)=1/2f(n-1) what is f(5)?

Answers

Answer:

10

Step-by-step explanation:

[tex]f(n) = \frac{160}{ {2}^{(n - 1)} } [/tex]

Answer:

This is 10

f(5) = 5f

Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased

Answers

Answer:$8.25 ÷ 3= x or 3·x =8.25

Step-by-step explanation:

3*x=8.25

Write a three digit number that gives same answer when rounded to the nearest ten and to the nearest hundred .explain

Answers

Answer:

Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, the nearest million, and so on. All the numbers to the right of the place you are rounding to become zeros. Rounded numbers are easier to remember and easier to use.

PLEASEEE!! HEPPPP!!

It takes Shonda of an hour to dry one load of laundry in her dryer. How many hours will it take her to dry 4 loads of laundry?

A. 1/5
B. 1 3/5
C. 3 1/5
D. 4/5​

Answers

Shonda takes an hour to dry one load of laundry.No of loads =4

No of hours

[tex]\\ \sf\longmapsto 4(1)[/tex]

[tex]\\ \sf\longmapsto 4 hours[/tex]

None of the above

what does n equal in 4n − 2n = 4

Answers

Answer:

Step-by-step explanation:

4 = 2

What is the vertical change from Point A to Point B?

What is the horizontal change from Point A to Point B?

What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth, if
necessary

Answers

Answer:

The vertical change is 1

The horizontal change is =2

The rate of change  .5

Step-by-step explanation:

Point A is at (2,1)

Point B is at (4,2)

The vertical( up and down) change is (2-1) = 1

The horizontal ( left and right) change is (4-2) =2

The rate of change is vertical over horizontal (1/2) = .5

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

1. Vertical change :

[tex]2 - 1[/tex]

[tex]1[/tex]

2. Horizontal change :

[tex]4 - 2[/tex]

[tex]2[/tex]

3. Rate of change :

[tex] \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex] \dfrac{2 - 1}{4 - 2} [/tex]

[tex] \dfrac{1}{2} [/tex]

[tex]0.5[/tex]

4. Lincoln began his speech, “Four score and seven years ago....” How many years is four score and seven? (Hint: A score is 20 years.) Can someone help me?​

Answers

87 years I think…. If a score is 20 years and four scores have passed you do 4x20 = 80. 80 plus the seven 80+7 = 87

Is it possible to construct a triangle with the side lengths of 6 cm 11cm and 13 cm why or why not?

Answers

Answer:

yes because....

Step-by-step explanation:

6 + 11 > 13

AAA help I need to do this for schoosleldkdk

Answers

Answer:

[tex] \frac{1}{8} [/tex]

Step-by-step explanation:

The total amount of cards is 8, and the stack have 4 even numbers, so the probability is

4/8 Simplify it and

1/2

Now, there are just 6 cars bigger than 6, so:

2/8. Simplify it

1/4

Now you have to multiply the two values:

1/2×1/4 = 1/8

look at the pictuse below i would copy and paste but I can't copy a picture

Answers

Answer:

I can't really see it so i don't know I'm sorry

Answer:

15

Step-by-step explanation:

find the value of a square + b square when a+b = 6 a_b = 4

Answers

Answer:

a+b=6

a-b =4

______subtract

(a-a)+(b-(-b))=6-4

0+2b = 2

b= 1

put the value of b at any equation

a+1 =6

then a=6-1=5

a square+b square= 25+1= 26

Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money

Answers

The acceptable and realistic ways to to change the confidence interval to contain zero are;

Martha should decrease x-bar by providing medicine to treat shock to the perfume users.Decrease sample size than 30Increase the confidence level, till the interval contains zero

Reasons:

The confidence interval is given by the following formula;

[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]

When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.

Therefore, Martha has to either intervene to reduce the mean also known as x-bar

Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero

Therefore;

Martha should decrease x-bar, [tex]\overline x[/tex], by providing medicine to treat shock to the perfume usersUse a much smaller sample size, n, such that [tex]t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}} > \bar{x}[/tex]

Increase the confidence level to 95% or 99%, thereby increasing the error bound

Learn more here:

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Jessie made 15 sales calls yesterday. Clay made n calls. If clay made 3 times as many sales calls as jessie, choose the equation thats shows how many sales calls clay made yesterday

Answers

It would be

N = 15 x 3

Answer:

n = (15)(3) = 45

Step-by-step explanation:

This problem is very simple, all we need to do is take the information we get and put it in equation form.

Jessie made 15 calls, Clay made 3 times as many as her. 15 times 3 is 45. Put in equation format it will look like:

n = (J) * (3)

n is how many calls Clay made, and J is how many calls Jessie made.

I need help ASAP! Is this linear increase decrease or exponential growth decay

Answers

Option B: Exponential growth

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.  

Option A is incorrect because y is not decreasing  

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

*EASY* I WILL GIVE BRAINLIST TO THE FIRST RIGHT ANWSER

Ruby is visiting San Francisco. From her hotel she walks 2 blocks east an 4 blocks north to a coffee shop. Then she walks 4 blocks west and 3 blocks north to a museum. Where is the museum in relation to her hotel?

here's the format for the answer if it helps : The museum is _ blocks _(West/East) and _ blocks _(South/North) of her hotel.

Answers

Answer:

Step-by-step explanation:

6. a + 6 < -2; a = -8
I
0. yes
P. no

Answers

Answer:

yes

Step-by-step explanation:


HELP !! Look at the photo please

Answers

Where is the photo bc in order for me to help you I need the picture

No links just answer
Simplify

Answers

Answer:

first option _32\21 is the answer

Step-by-step explanation:

the answer will

-32/21

I'm indian just came in Canada

indians are very intelligent in maths

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