Find all rational polynomials p(x) = x3 + ax2 + bx + c such that a, b, c are
roots of the equation p(x)=0

Answers

Answer 1

Answer:

p(x) = x³ +0x² +0x +0p(x) = x³ +x² -x -1p(x) = x³ -x² -2x

Step-by-step explanation:

If the roots of p(x) are a, b, c, then it factors as ...

  p(x) = (x -a)(x -b)(x -c)

and the expanded form is ...

  p(x) = x^3 -(a+b+c)x^2 +(ac +b(a+c))x -abc

The requirement that the coefficients match the roots means we have three equations in three unknowns:

  a = -(a+b+c)

  b = ac +b(a+c)

  c = -abc

The attachment shows the solutions to these equations. The solutions are found by making the substitutions ...

b = xc = ya = -(x+y)/2

This leaves us with two equations in two unknowns that can be graphed on a Cartesian plane. The graph of the second equation is a circle:

  x(1 -a -y) -ay = 0   ⇒   (x +1)^2 +y^2 = 1

The graph of the first equation is the union of the line y=0 and two hyperbolas. The points of intersection between this graph and the circle are ...

  (x, y) = (-2, 0), (-1, -1), (0, 0)   ⇒   (a, b, c) = (1, -2, 0), (1, -1, -1), (0, 0, 0)

The three polynomials that correspond to these values are shown above and in the attachment.

_____

Additional comment

There is an irrational fourth solution to the requirement that the roots match the coefficients.

Find All Rational Polynomials P(x) = X3 + Ax2 + Bx + C Such That A, B, C Are Roots Of The Equation P(x)=0

Related Questions

Which figure has reflection symmetry?

Answers

The bottom left figure

Answer:

the first option

Step-by-step explanation:

if you were to fold it in half it would be the same shape without anything poking out of the sides. one side reflects the other side

WILL GIVE BRAINLIEST
Select the graph of the solution. Click until the correct graph appears.



| x | = 2

Answers

Answer:

It is the second graph, the one with two filled in dots, but no line.

Step-by-step explanation:

The reason it is not the first one is because it has not filled in dots, AND no line, so it's basically saying there is no answer, which is not true.

The reason the third one (the one with a line) is wrong is because, for example, x cannot be 1, because 1 ≠ 2, and if there is a line, it should be true.

Answer:

its the awnser with the 2 not the -2

Step-by-step explanation:

Set up a proportion and solve for x.
1) If I can make up one test in 30 minutes, how long will it take me to make 11 tests?
Can you please help this is due tomorrow and it’s almost Christmas break:((

Answers

30x11 is 330.

300mins

Sorry i'm a little tired, if you want ask me how i got it and show my work in the comments. Thanks u

A Coke can has a radius of 4 cm and a height of 11 cm. What is the volume of the can?

Answers

Answer:

V ≈ 552.9 cm³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height ) , then

V = π × 4² × 11 = π × 16 × 11 = 176π ≈ 552.9 cm³ ( to the nearest tenth )

Answer:

The volume of Coke can is 552.64 cm².

Step-by-step explanation:

Given :

✧ Radius of Coke can = 4 cm.✧ Height of Coke can = 11 cm.

To Find :

✧ Volume of Coke can

Using Formula :

[tex]{\star{\small{\underline{\boxed{\sf{\red{V_{(Can)} = \pi{r}^{2}h}}}}}}}[/tex]

✧ V = Volume ✧ π = 3.14 ✧ r = radius ✧ h = height

Solution :

Here's the Coke can is in cylindrical form.

So, finding the volume of Coke can by substituting the values in the formula :

[tex]{\dashrightarrow{\pmb{\sf{Volume_{(Can)} = \pi{r}^{2}h}}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4)}^{2} \times 11}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4 \times 4)}\times 11}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(16)}\times 11}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {16}\times 11}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314}{100} \times {16}\times 11}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314 \times 16 \times 11}{100}}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{5024 \times 11}{100}}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{55264}{100}}}}[/tex]

[tex]{\dashrightarrow{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}[/tex]

[tex]\star{\red{\underline{\boxed{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}}}[/tex]

Hence, the volume of Coke can is 552.64 cm².

In how many ways can you arrange six trophies on a shelf?

Answers

Answer:

720 ways

Step-by-step explanation:

Assuming order doesn't matter, there are [tex]6!=6*5*4*3*2*1=720[/tex] ways to arrange six trophies on a shelf.

Which of the following

Answers

Answer:

which of the following what??

Step-by-step explanation:

..

Yolonda ran 4 times last week here are the distances she ran in km
17.9,6.03,15.66,3
What’s the total distance ran

Answers

Answer:

42.59 km

Step-by-step explanation:

Total distance = 17.9 + 6.03 + 15.66 + 3 = 42.59

Answer:

42.59 km

Step-by-step explanation:

When a question tells you to find the total of something it is usually means you need to add to add decimals you align the decimals and if a number doesn't have a decimal you add .0 on the end then line it up. It also might help to add a 0 in empty spots . Then you move the decimal to the same place in the solution and add like normal.

     

 17.90

 06.03

  15.66

+03.00

 42.59

Ethan was simplifying 3xl(-2xl + 1)2 State and correct the error below
3xl(-2x1 + 1)
(-6x²/²+3x1²
(-6x?[2 + 3x1)(-6x12 + 3xl)
-36X414 - 18x13 – 18x13 + 9x²12
-36X*1* 36x12 + 9x212
-36x* (1) – 36x®(-1) + 9x?(-1)
36x4 + 36x°– 9x2

Answers

Answer the mathematical

If g(x) =3-2x, find g(-1) (show work)

Answers

g(-1)=3-2(-1)
=5
Hence the correct answer should be 5

Which numbers are irrational numbers?
Select each correct answer.

Answers

the correct answer is B

Answer

Well pi is an irrational number because it can't be simplified into a fraction. And from what I can see neither can the sqaure root of 10/49. So I believe it would be both of them. But if there is only one answer than i'm not sure sorry. But it also says each so maybe there is more than one answer.

Step-by-step explanation:

An analyst surveyed the movie preferences of moviegoers of different ages. Here are the results about movie preference, collected from a random sample of 400 moviegoers.
A 4-column table with 4 rows. The columns are labeled age bracket and the rows are labeled type of movie. Column 1 has entries cartoon, action, horror, comedy. Column 2 is labeled children with entries 50, 22, 2, 24. Column 3 is labeled teens with entries 10, 45, 40, 64. Column 4 is labeled adults with entries 2, 48, 19, 74.
Suppose we randomly select one of these survey participants. Let C be the event that the participant is an adult. Let D be the event that the participant prefers comedies.
Complete the statements.
P(C ∩ D) =
P(C ∪ D) =
The probability that a randomly selected participant is an adult prefers comedies is symbolized by P(C ∩ D).

Answers

Using it's concept, it is found that the probabilities are given as follows:

P(C ∩ D) = 0.185.P(C ∪ D) = 0.5775.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 400 moviegoers.

From the table, 74 are adults who prefer comedies, hence:

P(C ∩ D) = 74/400 = 0.185.

2 + 48 + 19 + 74 = 143 are adults, while 24 + 64 = 88 are not adults but prefer comedies, hence the "or probability" is given by:

P(C ∪ D) = (143 + 88)/400 = 0.5775.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

0.3575

0.405

Step-by-step explanation:

can you help solve this? ​

Answers

Answer:

Step-by-step explanation:

Please Help Question in picture

Also please dm me on in sta : yourdealerjeremi
I could use help on a few more questions

Answers

Answer:

c) line VR is parallel to line ST

pls help me with my maths if you can​

Answers

Answer :

A) R- d✖️5= x

B) m/4 - b = x
Ok done. Thank to me :> ✅

Need help ASAP!!!!!!​

Answers

Answer:

graph b

Step-by-step explanation:

Help Asap I am stuck
suppose the value of an investment increases 12% per year and the investment has a current value of 33,00.00 which equation models the value of this investment after x years?

Answers

Answer:

bro pls someone hurry i need help

Step-by-step explanation:

what are the zeros of the function of y=x^2-3x+2​

Answers

Answer:

1 and 2

Step-by-step explanation:

Zeros of the function is where the function intersect with x-axis (or in other way the zeros of function is x value when y = 0 )

y=x^2-3x+2​

(we substitute y with zero)

0 = x^2-3x+2​

or in other way

x^2-3x+2​ = 0

Then we factor out the function by using the grouping method

(When we should give two numbers that there sum is equal -3 and if we multiply them we get 2)

and these two numbers are -2 and -1

x^2-3x+2​ = 0

*Substitute the middle term with -x-2x

x^2-x-2x+2​ = 0

*factor out x , then factor out -2

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

*factor out x-2

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

Either

x-2 = 0

So

x = 2

Or

x-1 = 0

So

x = 1

in conclusion the zeros of this function is 1,2

samuel goes to a store and buys an item that costs x dollars. he has a coupon for 15% off, and then a 6% tax is added to the discounted price. write an expression in terms of x that represents the total amount that samuel paid at the register.

Answers

Answer:

I think you might be able to work with this: 0.15 * x - x + x * 0.06

Step-by-step explanation:

The item's cost is X.

So he has a coupon for 15%, so the cost of the item times 0.15 = how much he's getting as a discount, for example: A toy robot costs 13.46, Jenny has a coupon for 25% off, to find out how much she paid, multiply 0.25 by 13.46 which equals about 3.37, so 13.46 - 3.37 = 10.09

So 0.15 (the coupon price) * x (the item's original price) - x (the items orignal price) + x * 0.06 (the sales tax)

Comment if you need any help T^T

Brainliest if correct! Please explain how this is done!
In ΔABC, ∠B is a right angle, AB = 30, and sec A = 5/3. Find the value of csc C in fraction and in decimal form.
I will mark brainliest if you are correct!

Answers

The value of csc C in fraction and in decimal form is as follows:

csc C  = 5 / 3

csc C = 1.66666666667

Using trigonometric ratio,

secant A = 1 / cos A = hypotenuse / adjacent

Therefore,

sec A = 5/3

sec A = 1 / cos A

cos A = adjacent / hypotenuse

cos A = 3 / 5

A = cos⁻¹ 0.6

A = 53.1301023542

Therefore,

∠A = 53°

∠B = 90°

∠C = 180 - 143 =  37°

cosec C = 1 / sin C = hypotenuse / opposite

cosec C = 5 / 3

learn more about trigonometry here: https://brainly.com/question/25942962?referrer=searchResults

please help and show work I'll mark you brainliest if I can ​

Answers

Answer: If your talking about the angle degree it is 45°

Step-by-step explanation:

evaluate p-q if p=14 and q=13

Answers

Answer:

Value of [tex]p-q=1[/tex]

Step-by-step explanation:

We need to find [tex]p-q[/tex]

[tex]p-q=14-13\\\\=1[/tex]

[tex]\huge\boxed{\sf{Hello\:there!}}[/tex]

We are asked to evaluate p-q.

Now, if we aren't given the value of every variable, evaluating this expression is impossible. However, we do have the value of p (14) and the value of q (13)

We plug these numbers instead of the variables:

p-q

p=14

q=13

14-13

1

Hence, the value of the expression is 1.

[tex]\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}[/tex]

[tex]\huge\bold{Good\:luck!}}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]


A music store purchases a grand
piano, wholesale, for $5,000.
They markup the retail price 65%.
What is the retail price?

Answers

Answer: 8250

Step-by-step explanation:

Answer:

8548

Step-by-step explanation:

NEED HELPPP ASAAPPPPPPP

Answers

Answer:

me too

Step-by-step explanation:

Find the equation of the line. Use exact numbers. y =__ x +__​

Answers

EXPLAIN:

Ex:  the line is:  y = ax + b

The line go through 2 points ( 0 ; -5 ) and ( 5 ; 0 )

So: [tex]\left \{ {{0=5a+b} \atop {-5=0a+b}} \right. =>\left \{ {{b=-5a} \atop {b=-5}} \right. =>\left \{ {{a=1} \atop {b=-5}} \right.[/tex]

The line: y = x - 5 = (1)x + (-5)

ANSWER: y = (1)x + (-5)

ok done. Thank to me :>

16 =
ОА. 4
ОВ. 3
ОС. 8
O D. 6

Answers

Answer:

A. 4

Step-by-step explanation:

I hope this helps you!!!

plss help me with this:(((​

Answers

7 is the slope :) -2 would be the y-intercept

Answer:

11) 7 ( Answer A)

12) (-2) ( Answer D)

Step-by-step explanation:

You can use y = m x + c to answer these questions.

In the equation y = m x + c,

m = slope

c = y - intercept

According to the question,

they have given the equation,

y = 7 x - 2

So, you can replace it with y = m x + c like this.

y = 7 x - 2

    ↑       ↑

    m      c

There fore,

slope = 7

y - intercept = ( - 2)

And now let's write the answers for the question.

11) 7 ( Answer A)

12) (-2) ( Answer D)

Hope this helps you :-)

If sixteen dried beans weigh one ounce, then how many dried beans wiring one pound

Answers

Answer:

96 dried beans will weigh one pound

16 beans in one ounce x 16 ounces in a pound = 256 beans total.

Help me, please! I'll give 20 points.

Answers

Answer:

A = 97.5

Step-by-step explanation:

Since A & B are supplementary, the general equation would be:

180 - 82.5 = A

A = 97.5

1. 5 3/4 + 5/6 + 2 1/2
2. 3 1/3 - (5 - 1 5/6)

Answers

Ok done. Thank to me :>

Please help, I will mark brainliest :)

Answers

Answer:

Its A $0.50 per mile

Step-by-step explanation:

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