Find a degree 3 polynomial with real coefficients having zeros 3 and 1 − 4i and a lead coefficient of 1. Write P in expanded form.

Find A Degree 3 Polynomial With Real Coefficients Having Zeros 3 And 1 4i And A Lead Coefficient Of 1.

Answers

Answer 1

[tex]\text{Let,}\\\\~~~~~~~x=1-4i,\\\\\implies x-1 = -4i\\ \\\implies (x-1)^2 =(-4i)^2\\\\\implies x^2 -2x +1 = -16\\\\\implies x^2 -2x +1 +16 = 0\\\\\implies x^2 -2x +17=0\\\\\text{So,}~ x^2 -2x +17 ~\text{is a factor of the 3 degree polynomial.}\\ \\\text{The polynomial is,}\\\\P(x) = (x-3)(x^2 -2x +17)\\\\~~~~~~~=x^3-2x^2+17x -3x^2 +6x -51\\\\~~~~~~~=x^3 -5x^2 +23x -51[/tex]


Related Questions

Pick one A,b,c,d,e will give brainlest

Answers

Answer:

E    (simalr to the other one you posted)

Step-by-step explanation:

Denominator cannot equal 0   so domain (x values) cannot include 2

  range: all numbers, buthere is no way to make a 0

-15 divided by -1 2/3

Answers

Answer:

9

Step-by-step explanation:

15 / 5/3 = 15 x 3/5=9

Because a negative numebr divided by a negative number is always positive.

Answer:

9

Step-by-step explanation:

Look at this rectangle. Find the value of u.

Answers

I hope I can help you:)

Answer:

1 inch

Step-by-step explanation:

We know that opposite sides of a rectangle are equal to each other.

Given that,

Perimeter = 30 in

Therefore,

u + u + 14 + 14 = 30

2u + 28 = 30

2u = 30 - 28

2u = 2

Divide both sides by 2.

u = 1 in

Which statement is true?
∞Σn=1 0.2(-3)^n-1 converges because r< 1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| <1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| > 1.
∞Σn=1 0.2(-3)^n-1 converges because r> 1.​

Answers

The mode of the ratio of the sequence should be greater than one for the divergence. Then the correct option is C.

What are sequence and series?

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

We know that the condition of the converges of the series will be given as

[tex]\rm \Sigma ^{\infty}_{n=1} \ 0.2(-3)^{n-1}\ \ diverges \ because \ |r| > 1.[/tex]

The mode of the ratio of the sequence should be greater than one for the divergence.

More about the series link is given below.

https://brainly.com/question/10813422

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Answer: It’s C

Step-by-step explanation:

Which expression is equivalent to 2(5z+3)?

Answers

Answer:

D

Step-by-step explanation:

That expression equals :

10z+6

So, now we need to find one of the expressions that ALSO gives us 10z+6

D

This is because:

2*3z=6z

2*2z=4z

----------------------

6z+4z=10z, so we got that one so far.

NEXT

2*3=6.

We got the 6 too!

it is d

which is more likely to have a mass close to 3 kilograms small feather a five year old cat or a grown elephant or a peach. dont delete this question dbs at brainly (dbs = drag on balls)

Answers

Answer:

5 year old cat

Step-by-step explanation:

because a kg is about a pineapple

1
N
3
5
6
B
10
56:0
What is the range of the function on the graph?
5
14
O all real numbers
O all real numbers less than or equal to -1
all real numbers less than or equal to 3
© all real numbers less than or equal to 0
-5-4-3-2-14
1 2 3 4 5 X
I
-2
-3
-4
-5

Answers

Answer:

pack you

pa brainliwa po

Find the greatest common factor of 8 and 24.

Answers

Answer:

8

Step-by-step explanation:

Factors of 8: 1, 2, 4, 8

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

They do share a few factors but the greatest one shared between the two is 8

Which graph of f(x) satisfies the conditions Limit of f (x) as x approaches 2 minus = –4 and Limit of f (x) as x approaches 2 plus = 0? HURRY WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!

Answers

The graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.

What is one-sided limit for function of single variable?

In rough terminologies, the limit from one side is when we only use one side of the function with respect to the considered point of interest (in input) to predict the value of the function at that point.

For this case, we need to find the graph of the function f(x) from the considered 4  graphs for which:

[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4\\\\\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]

For the first graph, for the point x=2, on left from the point x = 2 lies a ray. If thats the function, we can hope that the function will continue having the same line to the right too, so the prediction for value of function on x = 2 is the value that line gives for y.

That is -4.

Thus, prediction of function from left of x = 2 is -4, or

[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4[/tex]

Similar to that, from the right of the point 2, there is some yellow curve. That predicts that the function's value at point x = 2 should be 0 (the yellow curve seems like touching the x-axis where y = 0 at the point x=2.

Thus, we have:

[tex]\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]

So graph first is correctly pertaining such function f(x).

Second graph when refered, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]

Thus, its wrong graph.

Third graph when refered, we see that if we predict value at x =2 from left, the green line in the left will make us predict that the function would be -2 at x = 2 (see the green point in the third graph), so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = -2[/tex]

Thus, its wrong graph.

Similarly, for the fourth graph, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]

Thus, its wrong graph.

Thus, the graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.

Learn more about one-sided limits here:

https://brainly.com/question/23625942

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Answer:answer a

Step-by-step explanation: got right on edge 2023

What is the area of this trapezoid?

Answers

Answer:

The area is [tex]80[/tex]

Step-by-step explanation:

rectangle in the middle; 24

both triangles on the side; 56

In total; 80

Find the value of X.

Answers

Answer: 23

Step-by-step explanation:

What formula can we use to find the surface area of a rectangular prism? ​

Answers

Answer:

○ [tex]\displaystyle SA = 2lw + 2lh + 2wh[/tex]

Explanation:

A rectangle has four right angles, including two pairs of congruent edges, only containing two dimensions – height and length. Therefore, going three-dimensional, a rectangular prism has three dimensions – width, height, length. With this information, you should know what the answer is.

I am joyous to assist you at any time.

Sketch advertising firm charges $150 to design a full-color flyer and 12 cents per flyer to print the flyer. Rose's Sweet Shop spent $192 on the flyers for the grand opening. How many Flyers did she buy?​

Answers

Answer:

210

Step-by-step explanation:

First, we keep $150 on the back of our minds(or our paper).

Second, we would assume that Rose's would've designed the flyer at $150, making us determine how much flyers they bought for the remaining $42.

($192 - $150 = $42)

Now that we know all of this, we can begin.

12 x 5 is 60, so 60 cents makes 1 dollar.

So for every dollar, they can make 5 flyers.

If we do 5 x 42, we'll get the answer of 210, which is the amount of flyers she bought!

what is the answer 2⅓+⅚​

Answers

Answer:

3 1/6

Step-by-step explanation:

2+1/3+5/6

(1/3=2/6)

so 3/6+5/6 =  7/6

please show your work, tysm :D

~giving brainliest!~

Answers

Answer:

1/16th

Step-by-step explanation:

You can write this problem as a function of time.

Let x be the amount of acetaminophen that you start off with.

Let n be the amount of 2.5 hour intervals that have passed

x*0.5^n

The reason this function works is because with each 2.5 hour interval, you multiply the total product by another 1/2.

Plugging in 4(because 4 2.5 hour intervals in 10 hours), you get:

x*0.5^4,

which is x/16.

This shows that 1/16th of the acetaminophen is left in the body after 10 hours.

50 points+ Brainliest PLEASE SHOW WORK!!!!
(i can only give brainliest if at least 2 people answer)

Answers

Answer:

here

Step-by-step explanation:

we can do it by using the formula like

mean; efx÷n

median =n+1÷2

mode =which is more

range=highest-smallest

Answer:

Step-by-stwe can do it by using the formula like

mean; efx÷n

median =n+1÷2

mode =which is more

range=highest-smallestep explanation:

what is this number? 1,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050 WILL MARK BRAINLIEST

Answers

Answer:

that isn't a number

Step-by-step explanation:

Which choice is the solution to the inequality below?
8x < 24
O A. x< 24
O B. x> 24
C. x>3
O D. x<3

Answers

Answer:

D

Step-by-step explanation:

8x < 24

divide both sides by the coefficient of x

8x/8 < 24/8

x < 3

i would really like some help, factoring trinomials if you want an extra 50-100 points you could help with a previous question on my profile lol

Answers

Answer:

[tex]g) \left(5x-2\right)\left(3x+2\right)[/tex]

[tex]h)2\left(8a-9\right)\left(a-2\right)[/tex]

[tex]i)3\left(21n^2+42n+16\right)[/tex]

Step-by-step explanation:

Starting with g) [tex]15^2+4x-4[/tex]

Break the expression into group

[tex]=\left(15x^2-6x\right)+\left(10x-4\right)[/tex]

Now, Factor out [tex]3x[/tex] from [tex]15x^2-6x[/tex] which is now is [tex]3x(5x-2)[/tex]

Next, Facotr out [tex]2[/tex] from [tex]10x-4[/tex] which is now is [tex]2(5x-2)[/tex]

Thus,

[tex]=3x\left(5x-2\right)+2\left(5x-2\right)[/tex]

Factor common term 5x -2

[tex]\left(5x-2\right)\left(3x+2\right)[/tex]

-------------------------------------------------------------------------------------------------------------

Next we have [tex]h)16a^2-50a+36[/tex]

Factor out common term thus we have [tex]2(8a^2-25a+18)[/tex]

Factor again: [tex]8a^2-25a+18[/tex] now turn into [tex](8a-9)(a-2)[/tex]

[tex]=2\left(8a-9\right)\left(a-2\right)[/tex]

-------------------------------------------------------------------------------------------------------------

Lastly we have [tex]i)63n^2+126n+48[/tex]

Rewrite the following:

63 as 3 * 21

126 as 2 * 42

48 as 3 * 16

[tex]63n^2+126n+48[/tex]

Now cut out common term:

[tex]=3\left(21n^2+42n+16\right)[/tex]

-------------------------------------------------------------------------------------------------------------

~lenvy~

Answer:

(g)  [tex](5x-2)(3x+2)[/tex]

(h)  [tex](16a-18)(a-2)[/tex]

(i)  [tex]3(21n^2+42n+16)[/tex]

Step-by-step explanation:

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

Find 2 two numbers ([tex]d[/tex] and [tex]e[/tex]) that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]Rewrite [tex]b[/tex] as the sum of these 2 numbers: [tex]d + e = b[/tex]Factorize the first two terms and the last two terms separately, then factor out the comment term.

Question (g)

[tex]15x^2+4x-4[/tex]

[tex]\implies ac=15 \cdot -4=-60[/tex]

[tex]\implies d+e=4[/tex]

Factors of 60:  1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the two numbers (d and e) that multiply to -60 and sum to 4 are:

10 and -6

Rewrite [tex]4x[/tex] as [tex]+10x-6x[/tex]:

[tex]\implies 15x^2+10x-6x-4[/tex]

Factories first two terms and last two terms separately:

[tex]\implies 5x(3x+2)-2(3x+2)[/tex]

Factor out common term [tex](3x+2)[/tex]:

[tex]\implies (5x-2)(3x+2)[/tex]

Question (h)

[tex]16a^2-50a+36[/tex]

[tex]\implies ac=16 \cdot 36=576[/tex]

[tex]\implies d+e=-50[/tex]

Factors of 576:  1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576

Therefore, the two numbers that multiply to 576 and sum to -50 are:

-32 and -18

Rewrite [tex]-50a[/tex] as [tex]-32a-18a[/tex]:

[tex]\implies 16a^2-32a-18a+36[/tex]

Factories first two terms and last two terms separately:

[tex]\implies 16a(a-2)-18(a-2)[/tex]

Factor out common term [tex](a-2)[/tex]:

[tex]\implies (16a-18)(a-2)[/tex]

Question (i)

[tex]63n^2+126n+48[/tex]

Factor out common term 3:

[tex]\implies 3(21n^2+42n+16)[/tex]

This cannot be factored any further.

Solve the system of equations.

Answers

Answer:

3x+2y=24

Y=3

Substitute in the equation

3x+2(3)=24

3x+6=24

3x=24-6

3x=18

X=18/3

X=6

Which real-world scenario involves a right triangle?

Answers

Answer:

There are a few different scenarios

Step-by-step explanation:

Bathroom Tiles,Kitchen flooringTriangle Backsplash ( tile behind your sink in kitchenDrywall work if you need right edges, you will need a right triangleFinally any sort of contracting and Deck work

FROM- THE GENIUS ANSWERER

How many times larger is 8 x 10^9 than 4 x 10^3

Answers

Answer:

600

Step-by-step explanation:

10x9 =90

10x3=30

8x90=720

4x30=120

720-120= 600

3. The math exam scores for a class are shown below.
a
Make a data display. What percent of the scores are 90
and greater?
24, 68, 83, 75, 81, 99, 98, 80, 85, 70, 89, 92, 77, 96,
180, 64, 88, 96, 76, 88

Answers

Answer:

30 percent of the scores are 90 and greater

6 Jenny is y2 years old and her daughter Allyson is y years old, If Jenny lives to the age of 13y,
Allyson will be y years old. How old is Allyson now? (Note: the difference in ages must
remain constant.)

Answers

Answer:

Allison is 7 years now, Jenny is 49 yeas now. Check.  13y = 13*7 = 91 will happen in 91-49 = 42 years. Jenny will be 7 + 42 = 49 years old at that time.

Step-by-step explanation:

Leila had 160 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.

Answers

Answer:

160 - k dollars

Step-by-step explanation:

Hello!

If Leila has 160 dollars and spends the amount k, then you are therefore subtracting k from 160. This is because you are using the value of k from 160.

So the expression would be 160 - k dollars

[tex] \tt(6x4−2x3 +7x2 −x) + ( 7x4+ 2x3−5x + 7)[/tex]

[tex] \\ [/tex]

With Solution!!​​

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \tt \dashrightarrow \:\tt(6x {}^{4} −2x {}^{3} +7x {}^{2} −x) + ( 7x {}^{4} + 2x {}^{3} −5x + 7)[/tex]

[tex]\qquad \tt \dashrightarrow \:\tt6x {}^{4} −2x {}^{3} +7x {}^{2} −x + 7x {}^{4} + 2x {}^{3} −5x + 7[/tex]

Now, move all like terms aside :

[tex]\qquad \tt \dashrightarrow \:6 {x}^{4} + 7 {}x^{4} - 2 {x}^{3} + 2 {x}^{3} + 7 {x}^{2} - x - 5x + 7[/tex]

Add the like terms ~

[tex]\qquad \tt \dashrightarrow \:13 {}x^{4} + 7 {x}^{2} + 6x + 7[/tex]

Answer:

13(x)⁴ + 7(x)²-6(x) + 7

Explanation:

[tex]\hookrightarrow \sf (6x^4 -2x^3+7x^2-x)+(7x^4+2x^3-5x+7)[/tex]

remove the parenthesis

[tex]\sf \hookrightarrow 6x^4-2x^3+7x^2-x+7x^4+2x^3-5x+7[/tex]

group the variables

[tex]\hookrightarrow \sf 6x^4+7x^4-2x^3+2x^3+7x^2-x-5x+7[/tex]

add similar terms

[tex]\sf \hookrightarrow 13x^4+7x^2-x-5x+7[/tex]

simplify

[tex]\hookrightarrow \sf 13x^4+7x^2-6x+7[/tex]

Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the following could be used to calculate the coordinates for point B? 5 = square root of the quantity of x minus 6 all squared plus y minus 5 all squared 5 = square root of the quantity of x minus 5 all squared plus y minus 6 all squared 5 = square root of the quantity of x plus 6 all squared plus y plus 5 all squared 5 = square root of the quantity of x plus 5 all squared plus y plus 6 all squared

Answers

The distance of segment AB is the number of units on the segment

The equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

How to determine the equation?

The given parameters are:

A = (6,5)AB = 5 units

The distance AB is calculated using:

[tex]AB = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]

This gives

[tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

Hence, the equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

Read more about distance equations at:

https://brainly.com/question/7243416

Answer:

√(x-6)² + (y-5)²

Step-by-step explanation:

The Distance Formula is √(x2 - x1)² + (y2 - y1)²

If you plug in the known values, you get √(x - 6)² + (y - 5)²

This is our answer.

Hi can someone help me pls

Answers

Answer:

f(x) = 45x + 5

Step-by-step explanation:

The parking fee for a minibus at an event is $5 entering the parking lot. There is an extra charge of $45 per passenger.

The formula that simulates the parking fee for this sentence is

f(x) = 45x + 5

This is because 45x represents the charge per passenger and we are using addition because the $5 minibus parking fee; to enter the parking lot - increases the total cost of the parking fee.

How to graph the equation y=-x^2+6x-5 on the accompanying set of axes?

Answers

Answer: See attached

Step-by-step explanation:

    Given:

y = -x² + 6x - 5

   

    Since this is a quadratic function, we will have a parabola.

    Because our x² value is negative, this parabola will be a "frowny face" instead of a "smiley face" like the parent function.    

    The - 5 means we shift the function 5 units to the right from the parent function.

    See attached for our graph.

    What parent function am I mentioning?

The parent function of y = -x² + 6x - 5 is y = x²

0.7 is equivalent to what fraction

Answers

Answer:

7/10

Step-by-step explanation:

Fractional form of 0.7 is 7/10.

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Look at the graph:In which economic area(s) shown on this graph did the Confederacy experience higher costs than the Union? (A). Government expenditures and human capital (B). Human capital and property destruction (C). Property destruction only (D). Government expenditures only divide 2/3 by 1/5 into mixed nuber Where do most people in Central America live?O A coastal areas where they can rely on fishing and tradeO B. rural settlements where soils are good for farmingO C. river valleys with enough water for farmingO D. highland areas where temperatures are cooler The general revenue fund consists of which two parts?. What claim is made in is a penny saved worth anything What is the value of the expression below? 7 - 4+5 A. 14 B. 40 C. 50 D. 15 If you observe the upper right first molar to be excessively erupted relative to the rest of the teeth on the upper arch, you would describe the first right molar as: A softball player has had 8 base hits out of 25 at bats for a current batting average of 8/25 = .320. How many consecutive base hits does she need if she wants to raise her batting average to .400? Explain or show your reasoning. What relationship is it when one population captures and feeds upon another population? b. Lisa has 120 sweets. She gives 2 of them toher brother. How many sweets does Lisa have left I just have one more question what is the answer to this one? . Which phrase represents theexpression 8x + 5?eight times five plus a numberB five times a number plus eightCfive less than a numbermultiplied by eightD a number multiplied by eightthen added to five What is the constant of proportionality? Find the common ratio of the sequence.1,-1, 1,-1... The scale on a drawing reads 1/16^ prime prime =1^ prime .A2 inch long line representsA. 8 feetB. 16 feetC. 32 feetD. 64 feet The Moon is able to fully cover the Sun during a solar eclipse because of its current orbit. One million years from now, this will change because the Moon is slowly moving ____________ from the Earth.Answer the blank.PLEASE HURRY Which sentence should be rewritten to use the active voice?O A. The teacher counted the students to make sure everyone was onthe bus.aO B. Spending a little time in the sun can help the body build up vitaminD.O c. The biology lesson was studied by Caleb until he couldn't seestraight anymore.O D. Tai wrote three paragraphs of her essay before deciding to take abreak Please answer this question, will give brainliest!! Researchers have proposed the term _____ for the tendency of recent immigrants to the United States to resist assimilation and cling to familiar practices that give meaning to life. Choose one answer: A: 13+t=17B:13t=17Find the value of t that makes the equation true