Find a polynomial function of degree 3 with real coefficients and the numbers 6, 3i as some of its zeros.

Answers

Answer 1

Answer:

A polynomial function of degree 3 with real coefficients and the numbers 6 and i 3 as some of its zeroes is [tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex].

Step-by-step explanation:

A third-order polynomial in standard form is a sum of monomials with natural exponentials such that greatest degree of monomials is 3. This kind of polynomials is described by this definition:

[tex]p_{3}(x) =\Sigma\limits_{i=0}^{3} c_{i} \cdot x^{i}[/tex] (Eq. 1)

Where:

[tex]i[/tex] - Index of a sum component, dimensionless.

[tex]c_{i}[/tex] - i-th coefficient, dimensionless.

Where the highest value of [tex]i[/tex] is the degree of the polynomial.

In addition, the Fundamental Theorem establishes that all polynomials with real coefficients and degree higher than zero have a number of complex roots, an extension of the real set, equivalent to the degree of the polynomial itself.

In our case, we guarantee the existence of three complex roots, of which we know two of them: [tex]r_{1} = 6[/tex] and [tex]r_{2} = i\,3[/tex]. The polynomial can be represented as a product of three binomials:

[tex]p_{3}(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3})[/tex] (Eq. 2)

Where [tex]r_{1}[/tex], [tex]r_{2}[/tex] and [tex]r_{3}[/tex] are the roots of the third order polynomial.

If we know that  [tex]r_{1} = 6[/tex] and [tex]r_{2} = i\,3[/tex] and assume that [tex]r_{3} = -i\,3[/tex], the resulting polynomial is:

[tex]p_{3} (x) = (x-6)\cdot (x+i\,3)\cdot (x-i\,3)[/tex]

And by Algebra of real numbers we obtain the polynomial in its standard form:

[tex]p_{3}(x) = (x-6)\cdot (x^{2}+9)[/tex]

[tex]p_{3}(x) = x\cdot (x^{2}+9)-6\cdot (x^{2}+9)[/tex]

[tex]p_{3}(x) = x^{3}+9\cdot x -6\cdot x^{2}-54[/tex]

[tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex]

A polynomial function of degree 3 with real coefficients and the numbers 6 and i 3 as some of its zeroes is [tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex].


Related Questions

Robert and Dora need to write 4,300,000,000 using scientific notation. Robert claims that 4,300,000,000 = 4.3 x 108 and Dora claims that 4,300,000,000 = 4.3 x 109. Which of the following best describes whose number is correct and the reason it is correct?

Answers

Answer:

Robert is correct

Step-by-step explanation:

we know in scientific notation a positive number goes to the right and if we do 4.3 and we go back the spaces it would be nine spaces so it would be 4.3 X 109

If x = 34, y = 53, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.


0.74 units
1.17 units
1.64 units
2.14 units

Answers

Answer:

2.14 units

Step-by-step explanation:

TO FIND AB:

sin 34=AC/AB

AB=AC/sin34=4/sin34=7.15

TO FIND AD:

sin 53=AC/AD

AD=AC/sin53=4/sin53=5.00

difference in length:

AB-AD=7.15-5.00=2.14 units

Answer:

the answer is 2.14 units

Step-by-step explanation:

took the test and got it right

Brainliest pls

Can someone help me I really need it

Answers

Answer:

No, the figures are similar but not congruent as although width is same, length of fig A is 3 blocks while length of fig. B is 4 blocks. For two fig. to be congruent, their l and b should be eql.

Hope u find this ans useful.

Pls mark me brainliest

Evaluate $\frac{33}{33\frac 13}$. Express your answer as a fraction in simplest form. (Thus the numerator and denominator should be integers whose greatest common divisor is $1$.)

Answers

Answer:

[tex]\dfrac{99}{100}[/tex]

Step-by-step explanation:

We need to evaluate [tex]\dfrac{33}{33\frac 13}[/tex]. Here, 33 is numerator and [tex]33\dfrac{1}{3}[/tex].

Firstly, we will solve the denominator.

[tex]33\dfrac{1}{3}=\dfrac{33\times 3+1}{3}\\\\=\dfrac{100}{3}[/tex]

The given expression becomes,

[tex]\dfrac{33}{33\frac 13}=\dfrac{33}{\dfrac{100}{3}}\\\\=\dfrac{33\times 3}{100}\\\\=\dfrac{99}{100}[/tex]

Hence, the required answer is 99/100.

A car rental company charges a daily rate of $ 23 plus $ 0.20 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $ 44.00. How many miles did you drive?

Answers

Answer:           105 miles

(44-23)/0.20

Your office window is a = 55 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 700 horizontal feet from your office. You know that the statue is c = 225 feet from the building. How tall is the statue? (See the figure below. Round your answer to two decimal places.)

Answers

Answer:

nothing

Step-by-step explanation:

nothing will come because there is no figure

HELP!!! Which of the following best describes the slope of the line below?

Answers

Answer:

C. Negative

Step-by-step explanation:

A quick reminder: an undefined slope makes the line vertical, a slope of 0 makes the line horizontal, a positive slope makes the line go up as x increases, and a negative slope makes the line go down as x increases.

In this case, the line is going down as x increases, meaning the slope must be negative.

2(x-5)=4x+7
solve for x

Answers

Answer:

x=-6

Step-by-step explanation:

Find the value of x.

Answers

Answer:

x=21

Step-by-step explanation:

180-126=54

54-12=42

42/2=21

x=21

What is the correct decimal point placement for the product of 3.54 × 15.42? 54.5868 545.868 5458.68 54586.8

Answers

9514 1404 393

Answer:

  54.5868

Step-by-step explanation:

The multiplicands each have 2 digits to the right of the decimal point, so the product will have 2+2 = 4 digits to the right of the decimal point. The correct placement is ...

  54.5868

__

Another way to tell is that the product is in the neighborhood of 3·15 = 45, which is nowhere near 545 or 5458 or any higher value.

Answer: 54.5868

Since 3 x 15 is already 45, now we have to multiply the decimals, but we must put a point.

.54 x .42 = 9.5868

45 + 9.5868 = 54.5868.

Hope this helps!

Find the value of x.
(7x + 16)
80°
The value of x is

Answers

i plugged it into conects & it told me this, hope it helps

answer for brainliest ! <3

Answers

Answer:

1: p=(2,4) q=(1,1) r=(5,2)

2 I am so sorry. the changing in the shape is not any transformation I've heard of before.

3:90 degree rotation (Counterclockwise.)

4: 180 degree rotation (doesn't matter which way.)

5: 90 degree rotation (clockwise)

6: Up 9 units, over 2 units to the right.

Hope this helps!!

Which of the following functions has a graph that passes through the origin? Select all that apply.
A. power; y equals x superscript n baseline
B. root; y equals Root Index n Start Root x End Root
C. reciprocal; y equals Start Fraction 1 over x End Fraction
D. exponential; y equals b superscript x baseline

Answers

Answer: a and b

power and root

3+3+3
Please Help....

Answers

Answer:

9

Step-by-step explanation:

3+3+3= 9 or you could just do 3x3

This is what I meant to ask lol

Answers

Answer:

false

Step-by-step explanation:

theyre not proportional because 100*2=200 but 35*2 is not 45 :)

Answer:

True

Step-by-step explanation:

The miles column is increasing steadily by 100The cost column is increasing steadily by 10Neither column is changing the amount that's being increased and neither is decreasing after an increase, therefore, the answer is true.

I hope this helps!


Write a number that has a 3 that is 10
times the value of the 3 in 7.31
Your answer

Answers

Answer:

3

Step-by-step explanation:

7.31

3 in the tenths place

3 = 3/10 or 0.3

0.3*10=3

answer : 3
explain: 7.31
3 is in 10 place so
3= 3/10 or 0.3 ;)

Are these ratios equivalent?
16 shipments every 6 years
8 shipments every 3 years
yes
no

Answers

Answer: Yes

Step-by-step explanation:

If you do 16/6 you get 2.667 and if you do 8/3 you also will get 2.667

describe the steps to determining and graphing a translation.

Answers

Answer:

A TRANSLATION OF A GRAPH is its rigid movement, vertically or horizontally. On the left is the graph of the absolute value function. On the right is its translation to a "new origin" at (3, 4). y = |x|.

Create a word problem using the math sentence below. Make sure you write in complete sentences. -25 + (-35)

Answers

Step-by-step explanation:

john put 25 dollars in a jar and his wife put 35 dollars in the savings jar as well so save for there trip coming up

Answer:

Sally borrowed twenty-five dollars from Alex to buy a movie at the store. Later, she borrowed another thirty-five dollars to buy ride tickets at the state fair. How much money does she owe Alex?

Step by-step explanation:

When you have an even number of negative numbers in an equation, the answer will always be positive. When there's an odd number of negative numbers, the answer will be negative. For a problem like this, you can ignore the negative signs and focus on the numbers. 25+35 is 60, so Sally owes Alex 60 dollars.

                  Hope this helps!


Evaluate:

54 - 75 + 81 - (-27) + 53

Answers

Answer:

140

Step-by-step explanation:

Answer:

140.

Step-by-step explanation:

PEMDAS.

Since there isn't any problems that aren't adding, we can just do it step by step.

54 - 75.

-21.

Add 81.

60.

Subtract -27.

87.

Add 53.

140.

Brainiest?

Consider the sequence of steps to solve the equation:
7x
5(x - 3) =
Step 1 = 10(x - 3) = 7x
Step 2 = 10x - 30 = 7x
Step 3 = 3x - 30 = 0
Step 4 = 3x = 30
Step 5 = x= 10
Identify the property of equality which yields Step 5.

A)
Division Property
B)
Addition Property
C)
Subtraction Property
D)
Multiplication Property

Answers

The answer is d I’m pretty sure
I think it is D for sure

Find the value of x:

Answers

X equals 14 because D+ he is 14°
X = 14 use the graph

I NEED THIS NOW! PLZ HELP! 1ST GETS BRAINLIEST! PLZ USE THE 3-READ PROTOCOL
manny has 1/2 of a yard of a fabric with which he intends to make bookmarks. each bookmark is made from 1/8 yard of fabric. how many bookmarks can manny make?

Answers

Answer:

Manny can make 4 bookmarks

Step-by-step explanation:

1/2 ÷ 1/8 = ?

(flip the second fraction and multiply)

1/2 x 8/1 = 8/2 = 4

Please help me I have no idea what the answer is

Answers

Answer:

hi

Step-by-step explanation:

IDK WHY IT SAYS IM A COLLEGE PERSON IM NOT BUT UM I NEED HELP WITH THIS PLEASEEEEEE

Answers

Answer:

option 3

Step-by-step explanation:

Answer:

it's option 3 i think

Step-by-step explanation:

3. A change machine contains nickels, dimes, and
quarters. There are 75 coins in the machine, and the
value of the coins is $7.25. There are 5 times as
many nickels as dimes. How many quarters are in
the machine?
Equation #1:
Equation #2:
Equation #3:
# of quarters:

Answers

Answer:

50 nickels 10 dimes 15 quarters

Step-by-step explanation:

im pretty sure

f(x)=2|5x+7|−1, evaluate f(−4)

Answers

Answer:

Step-by-step explanation:

f(x) = 2 |5(-4)+7| -1

     = 2 |(-20)+7| -1

     = 2 | -13 | -1

     = 26 - 1

     = 25

A function assigns the value of each element of one set to the other specific element of another set. The value of the function f(-4) is 25.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The value of f(-4) can be evaluated by substituting the value of x as -4 in the given function, therefore, the value of f(-4) can be written as,

f(x) = 2|5x+7| − 1

f(-4) = 2|5(-4)+7| − 1

      = 2|-20 + 7| - 1

      = 2|-13| - 1

      = 2(13) - 1

      = 26 - 1

      = 25

Hence, the value of the function f(-4) is 25.

Learn more about Function here:

https://brainly.com/question/5245372

#SPJ2

Find value of x, first gets brain

Answers

Answer:

53

Step-by-step explanation:

Pls help me slove this -2 1/3 - (-5) =

Answers

Answer:

4/3

Step-by-step explanation:

-2 1/3= -7/3

-5=-15/3

Answer:

If I'm reading this correctly, -2.33 or -2 1/3 - (-5) should equal to 2 2/3

Step-by-step explanation:

Since a minus sign is close to the minus sign inside the parantheses, you should turn the minus sign into a plus, giving you -2 1/3 + 5 which should equal to 2 2/3. Hope this helps

(y^3)^2 without exponents​

Answers

Answer:

y^6

Step-by-step explanation:

Answer:

[tex]y^{6}[/tex]

Step-by-step explanation:

Step 1:

( y³ )²       Equation

Step 2:

[tex]y^{3 * 2}[/tex]        Multiply

Answer:

[tex]y^{6}[/tex]

Hope This Helps :)

Other Questions
A college campus has a lawn shaped like a circle with a radius, r, of 60 meters. Which is the best approximation of the area, A, of the circular lawn? (Use A=r2; is approximately 3.14.)Answers: A. 180 square meters B. 360 square meters C. 2,800 square meters D. 11,300 square meters Summarize the central idea of the text. Answer in 2-3 sentences. Tornadoes are violent storms that come from powerful thunderstorms.They appear as a funnel- or cone-shaped cloud with winds that can reach up to 300 miles per hour. They cause damage when they touch down on the ground. They can damage an area one mile wide and 50 miles long. Tornado season commonly occurs during the months of March through August, but they can occur at any time. They can happen in any state but are most commonly found in Arkansas, Iowa, Kansas, Louisiana, Minnesota, Nebraska, North Dakota, Ohio, Oklahoma, South Dakota, and Texas. This area is commonly called "Tornado Alley."If there are weather or news reports that say there is a tornado in your area, the most important thing to do is to take shelter immediately in a place without windows, such as a bathroom or a basement. A Tornado Watch means that tornadoes are possible. Stay tuned to the radio or television news. A Tornado Warning means that tornado has been sighted. Take shelter immediately! CAN SOME PLZ ANSWER THE TABLE IM GIVING BRAINLIEST PLEASE HELP Identify the slope (m)and y-intercept (b) of the linear function graphed below. Then, construct the linear equation for What is the minimum point of the graph of the equation y = 5x2 - 30x? Choose the best translation:scheduleO promocinO perezosoO horarioO impuestos - What value of x makes this equation true?0.5x -8= 0.2x + 7 What is the role ofelectrons within anatom?A.Electrons are in the nucleus and have anegative chargeB. Electrons are in the nucleus and have apositive chargeC. Electrons are outside the nucleus andhave a negative chargeD. Electrons are outside the nucleus andhave a positive charge How did this visual aid help you to visualize the information in the article? Describe the three ways to restore values that were lost in China during the time of the warring states. I need help asp . I'm running out of time HURRRY PLLEEASSSSEEE!!! x^2-6x +3 Hey can this be factored? If so what would be the answer? Thanks :) pls somebody help me with this question Find the values for x so that the perimeter of this rectangle is no greater than 150 centimeters Is 5O2 a Element or Compound? Sugar, C6H12O6, is made of carbon, hydrogen, and oxygen atoms. Sugar is (I WILL MAKE U BRAINLIESTA. a compound because it is made of two or more atoms chemically combined and its parts cannot be separated by physical meansB. a mixture because it is made of different kinds of atoms but they are not chemically combinedC. a solution because it dissolves when mixed with waterD.an element because it is a pure substance whose parts cannot be separated What was the name of the new vessel used by Europeans to explore?A. CompassB. CaravelC. AstrolabeD. Telescope -3,-8,-13,-18 write an equation for the nth term then solve A package of 3pairs of insulated gloves cost $17.97. What is the unit price of the pairs of gloves