Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros −6 and 1 + i.

Answers

Answer 1

Answer:

[tex]Q(x) = x^3 + 4x^2 - 10x + 12[/tex]

Step-by-step explanation:

Complex numbers:

The most important relation when dealing with complex numbers is that:

[tex]i^2 = -1[/tex]

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Q has degree 3 and zeros −6 and 1 + i.

Complex roots are always complex-conjugate, which means that if 1 + i is a root, 1 - i is also a root.

I am going to say that the leading coefficient is 1. So

[tex]Q(x) = (x - (-6))(x - (1 + i))(x - (1 - i)) = (x + 6)(x^2 - x(1-i) - x(1+i) + (1+i)(1-i)) = (x + 6)(x^2 - 2x + 1 - i^2) = (x + 6)(x^2 - 2x + 1 - (-1)) = (x + 6)(x^2 - 2x + 2) = x^3 + 6x^2 - 2x^2 - 12x + 2x + 12 = x^3 + 4x^2 - 10x + 12[/tex]

The polynomial is:

[tex]Q(x) = x^3 + 4x^2 - 10x + 12[/tex]


Related Questions

pls send this answer pls pls pls
no fake answer pls pls

Answers

Answer:

6.75×10^5

Step-by-step explanation:

that's the answerrr

Answer:

6.75x10^5

Step-by-step explanation:

Solve the system by substitution.

Y=3/4x-3
Y=1/4x+1

Answer must be in (y,x) or something like that
Will mark brainliest if correct.

Answers

As we know y=3/4x-3
Let's put it in the second equation
3/4x-3=1/4x+1
3/4 x -1/4 x = 1+3
2/4 x = 4
X= 4*4/2
x=8
Put x= 8 in first equation
y= 3/4 *8 -3
y=6-3
y=3
Check the answer
3=3/4 *8 -3
3=6-3
3=3
Correct
So(y, x) = (3,8)
Because x=8 and y=3

Need help with math again ​

Answers

Answer:

x=15

Step-by-step explanation:

x=√(12)²+(9)²

x=√144+81=√225

x=15units

PLS HELP what expression is equivalent to 2 + y + y + y + y + y +3?

Answers

Answer:

5y+5

Step-by-step explanation:

I hope this is right

[ASPS]WILL GIVE BRAINLIEST

Answers

Answer:

hi

Step-by-step explanation:

you should know that the sum of interior angles of a hexagon is 720 so

[tex]4x - 10 + 2x + 8 + x - 12 + 7x + 3x + 135 = 720 \\ 17x = 121 \\ x = \frac{121}{17} = 7.11764[/tex]

what's
[tex] \sqrt{ {25}^{2} - 15 {}^{2} } [/tex]

Answers

I’m pretty Sure that the answer would be 20 because 25 to the power of 2 would be 50 and 15 to the power of 2 is 30 and 50 - 30 =20

Answer:

20 Ans ..

Step-by-step explanation:

Given:

=25²-15²

Solution:

= √625-225

= 20 ans .....

An online games club charges $5.75 for the first game download and $2 for each additional
download per month. Write a rule for describing the total monthly fees f as a function of
additional downloaus d. What are the fees for 15 game downloads in a month?

Answers

Answer:

a) The rule is;

f = 5.75 + 2d

b) f = $33.75

Step-by-step explanation:

Here, we want to write a rule

The rule is that we have a standard download fee of 5.75 for the first download, and then a download fee of $2 per download for the rest

We have this as;

f = 5.75 + 2(d)

f = 2d + 5.75

Now for 15 downloads;

first download is $5.75, remaking 14 is at a rate of $2 per one

Thus, we have the fee value as;

f = 5.75 + 2(14)

f = 5.75 + 28 = $33.75

if a parallelogram is 1.9ft at its base and 1.5 at its height what's its area?

Answers

Answer:

2.85 ft²

Step-by-step explanation:

1.9 x 1.5

what's the value of a ?
[tex]a {}^{2} = 196[/tex]

Answers

ANSWER :

▶️a = √196

▶️a = 14

VARIFICATION :

▶️ 14² = 14×14

▶️ 14² = 196

hence , 14 is the answer..

Help me please , due soon

Answers

Answer:

Radius=12cm

Diameter=24cm

Step-by-step explanation:

The diameter is the full length of the circle through the middle (which is shown in the picture as 24cm).

The radius is half of the diameter.

Answer:

radius is 12 cm

diameter 24 cm

Landon owns 16 baseball cards, which is 4 times as many as Phillip owns.
The equation 4p=16 represents this situation where p is the number of baseball cards Phillip owns.
Which number line represents the solution to the equation?

Answers

Answer:

B

Step-by-step explanation:

i'm probably wrong but based on the information they give you the most likely answer has to be B. ok- well if you think abt it landon has 16 cards and that's 4 times as many as phillip has. so, phillip's cards could range anywhere between 4 and 16-

sorry if i'm incorrect :/ hope you get a good score or whatever tho

What is this supplementary angle?

Answers

Answer:

Step-by-step explanation:

Supplementary angles sum to 180 degrees.

x+118=180

x=62 degrees

Answer:

62°

Step-by-step explanation:

A supplementary angle is 180°.

180-118= 62

Graph the equation
y = -3. Determine the
slope of the line

Answers

Answer:

The slope is 0

Step-by-step explanation:

The line is horizontal.  All horizontal lines have a slope of 0.

The graph is attached.

Dylan hikes 90 miles in 3 days. At that rate, how many days does it take him to hike a total of 240 miles?

Answers

Answer:

8 days

Step-by-step explanation:

90/3 = 30 mi/day

240/30 = 8 days

Answer:

it will take him 8 days (7.98 in you don't round)

Step-by-step explanation:

90 -240= 150

150/90 = 1.6666....

1.66 * 3  = 4.98

4.98+3 =7.98  (8 if you round)

Describe how math in middle school differs from
high school math class?

Answers

high school math classes are more advanced than middle school math classes
High school math classes are a higher difficulty level, but most of what you learned in middle school math classes is used. It’s best to remember what you learned because you will end up using it in high school.

PLZZ HELPPPP QUIICKK :))

Answers

Answer:

A...................


HELP HELP HELP HELP HELP!

Distribute the following expression, and type the equivalent expression into the text box.

3(12x-6)

Answers

Answer: thanks for brainly points kid

Step-by-step explanation:

The endpoints of a line segment are (–1, 6) and (8, 6). What is the length of the line segment?

A.
2 units

B.
7 units

C.
9 units

D.
12 units

Answers

C. 9 units. It takes 9 units to get from-1 to 8

The height, h, of a plant (in inches) w weeks since it was planted is represented by the equations h=3w+3. How many weeks will it takes the plant to reach one foot.

Answers

Answer: 3 weeks

Step-by-step explanation:

We have to note firstly that 12 inches = 1 foot.

The equation given to represent the height in the question, h = 3w + 3.

The number of weeks that it will take the plant to reach one foot will then be:

h = 3w + 3

12 = 3w + 3

3w = 12 - 3

3w = 9

w = 9/3

w = 3

It'll take 3 weeks

I need help with this can anyone please help

Answers

Answer:

56

Step-by-step explanation:

4*7*2 is 56

Hope that helps and please tell me if I am wrong

I need help please, If triangle JKL is congruent to QRS, find each missing value

Answers

Answer:

x = 5, y = 17, z = 8

Step-by-step explanation:

   Since the triangles are congruent to each other, corresponding angles and sides are congruent to each other.

JL corresponds with QS so...

3x - 1 = 14

3x = 15

x = 5

RS corresponds with LK so...

y + 10 = 27

y = 17

Angle L corresponds with angle S so...

180 - 58 - 87 = 4z + 3

35 = 4z + 3

32 = 4z

z = 8

SOMEONE PLEASE HELP ME

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

a) Any set of functions that has a total degree of 4 and a total number of x-intercepts of 4 will do. Shown in the first attachment are 4 linear functions. A quadratic function with two x-intercepts could replace two of the linear functions, or a cubic with 3 x-intercepts could replace 3 of the linear functions.

__

b) Again, the total degree must be 3. Since there can only be one x-intercept, the quadratic factor must have none. A possible choice is shown in the second attachment.

Can someone help me with this

Answers

Answer:

B

Step-by-step explanation:

i think its B because the your line is in the negatives and to be specific in -5

and the line that is going to the right that means it is going to the positive so its positive infinet

Hope it's correct

Answer:

hi

Step-by-step explanation:

i think its B

you should inverse the function from x=y line

i cant explain in enlish better than this

hope this helps

if have more questions just ask

Math please help im failing this class its algebra

Answers

Answer:

y=5x+2

Step-by-step explanation:

-5x-4y=-8

-5x+y=2

y=2+5x

y=5x+2

it would mean so much if u help me out on this one!
im failling all my clases and i do online school so everything is horrible
plzzz help

Answers

Answer:the answer should be B :) !

Step-by-step explanation:

You need to add all the yards ran per day to get 112 then multiply by 3 since a yard is equal to 3 feet, getting 336.

pls :,) i’m begging u

Answers

Answer would be C. (-2,0) (0,3)
Y= -2/3 - 3
Mark the first guy Brainliest he got it right

Please Help Quick ASAP Hurry
Figure ABCD is a parallelogram.Which statement must be true?
a. AB is congruent to BC
b. AB is parallel to BC
c. AD is parallel to BC
d. \ is congruent to \C

Answers

Answer:

Step-by-step explanation:

Answer:

a. AB is congruent to BC   Not True

b. AB is parallel to BC        Not True

c. AD is parallel to BC        True

d. \ is congruent to \C        Not True

Step-by-step explanation:

The regualar price of a pair of sneackers
is $55 they are on sale for 25%

Answers

Answer:

$41 is your answer

Hope it Helps :)

Answer:

$41.25

Step-by-step explanation:

If the shoes regular price was $55 and the shoes are having a sale for 25%, this is how you would do the math.

25% is 25/100 or .25

55 * .25 = $13.75

55 - 13.75 = 41.25

pls help me I don't understand​

Answers

Answer:

[tex]d. \: \: \: 25 {x}^{6} [/tex]

Step-by-step explanation:

Given,

Side of the square

[tex] = 5 {x}^{3} [/tex]

Therefore, area of the square = side × side

[tex] = {5x}^{3} \times 5 {x}^{3} [/tex]

[tex] = 5 \times 5 \times {x}^{3 + 3} [/tex]

[tex] = 25 {x}^{6} [/tex]

The formula for calculating the area of a square is A=a^2. (a=side)
There are multiple ways to solve this but I’m gonna use the simple way to explain.
All we have to do here is take the side times the side:
5x^3•5x^3
5•5=25
**Careful** exponents are added, not multiplied.
25x^6 is the answer

Mr John leased two thousand fifty meter square of land from the city administration. He gave one eighth of his land to his brother. How many meters square did he have left?

Answers

Answer:

1793.75 m²

Step-by-step explanation:

Given that :

Total amount of land leased = 2050 m²

Fraction of land given to brother = 1/8

Amount of land given to brother :

1/8 * 2050 = 256.25 m²

Amount of land left :

2050 m² - 256.25 m²

= 1793.75 m²

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