Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3−i.

Answers

Answer 1

Answer:

[tex]P(x) = x^3 - 10x^2+ 34x-40[/tex]

Step-by-step explanation:

Given

[tex]p =1[/tex] -- Leading coefficient

[tex]Zeros: 4\ and\ 3 - i[/tex]

Required

Determine the polynomial

Represent the zeros with a and b

Such that

[tex]a = 4[/tex]

[tex]b = 3 - i[/tex]

The polynomial is:

[tex]P(x) = p * (x - a) * (x - b)[/tex]

[tex]P(x) = 1 * (x - 4) * (x - (3 - i))[/tex]

However, to solve further: We need to symmetrise over 3-i  and its conjugate

[tex]P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))[/tex]

[tex]P(x) = (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\[/tex]

To define a suitable function, the expression becomes

[tex]P(x) = (x - 4) * ((x - 3)^2+1)[/tex]

[tex]P(x) = (x - 4) * ((x - 3)(x - 3)+1)[/tex]

[tex]P(x) = (x - 4) * (x^2 - 6x + 9+1)[/tex]

[tex]P(x) = (x - 4) * (x^2 - 6x +10)[/tex]

Open bracket

[tex]P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40[/tex]

[tex]P(x) = x^3 - 6x^2 - 4x^2+10x + 24x-40[/tex]

[tex]P(x) = x^3 - 10x^2+ 34x-40[/tex]


Related Questions

Please help which shape has 4 lines of symmetry

Answers

The square is the right answer

Answer: yes she is right the left blue shape on bottom because

Step-by-step explanation: the four lines in the square horizontal vertical left side lines and right side lines   and lines of symmetry are sides the same looking if you fold them. hope that helped

4. Write the ratio for cos M.

cos M = 24/25
cos M = 12/25
cos M = 24/7
cos M = 25/24

Answers

Answer:

24/25

Step-by-step explanation:

Hello There

[tex]cos = \frac{adjacent}{hypotenuse} [/tex]

The adjacent of M is 24 and the hypotenuse is 25 so

[tex]cosm = \frac{24}{25} [/tex]

Answer:

cos M= base/hypotenuse=KM/LM=24/25

bleachers in a stadium are 4 meters tall and have a length of 12 meters. Calculate the measure of the angle formed by the bleachers and the ground

Answers

Answer:

right angle

Step-by-step explanation:

90 degrees

1 length is 4 that goes directly upwards

the other goes horizontle and their intersection is a 90 degree angle I THINK i've never really done these before.

Need help fast for 1 2 3 and 4 for please and thank you

Answers

The formula for the area of a circle is [tex]\pi r^2[/tex]

So if we have the first one...[tex]3.14*5^{2}[/tex]≈78.5

Now you can solve the other ones with this formula! Good luck!

The diameter of a sphere with a volume of 121.5 cubic mm is ___ mm.

Answers

Answer:

Diameter= 6.15

Step-by-step explanation:

Like the radius explanation but multiply the answer by 2.

‼️YALL I NEED HELP PLEASE HELP DUE IN 20 MINUTES ‼️

Answers

The line (in Standard Format, Ax+By=C) is 3x+6y=-17 [note: Convention is that x-coefficient is positive].
The slope of this line is (-A/B)=(-3/6)=-1/2.

All perpendicular lines have a negative reciprocal slope: 2
The equation of the perpendicular line is: 6x - 3y = D
[switch A and B and make negative; and we need point (6,3) to determine D]
6(6)-3(3)=D
36 - 9 = D
27 = D

The perpendicular line is:
6x - 3y = 27
or 2x - y - 9

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

I am pretty sure it is The third answer choice X < 8
It’s the first answer choice

what % of 276 = 77.28

Answers

Answer:

28%

Step-by-step explanation:

you can divide 276 by 100 to get how much each individual percentage is worth so when you multiply that number by 28 you get 77.28

Given f(x) =1 - 3/4x find the following.
a. f(-12) b. f(0) c. f(4)

Answers

Answer:

a. f(-12) = 10

b. f(0) = 1

c. f(4) = -2

Step-by-step explanation:

In order to find the function of each of these numbers, you just need to replace them in the function as x and then solve:

a. f(-12) = 1 - 3/4(-12)

 - f(-12) = 1 - (-36/4)

 - f(-12) = 1 + 9

 - f(-12) = 10

b. f(0) = 1 - 3/4(0)

 - f(0) = 1 - 0

 - f(0) = 1

c. f(4) = 1 - 3/4(4)

 - f(4) = 1 - 12/4

 - f(4) = 1 - 3

 - f4) = -2

Please help me out! (Find the measurements of the following angles. Fill in the blanks with your answer. Your answer should be numerical)

Answers

Answer in the file below

PLEASE HELP FAST! Which inequality is graphed below?

Answers

Answer:

I gotchu, it's A. x > -2

Step-by-step explanation:

The circle on the line is open so it means less than or greater than. If it was a close circle, it would be less than or equal to and vice versa. And the number is -2. The line excludes -2 but includes all numbers greater than that. So the answer would be A. x > -2

Answer:

a

Step-by-step explanation:

when the circle is open and not filled in means its not equal to and since -2 less than x, x=-3 or more

Sorry if im wrong


ANSWER AND SHOW WORK PLEASE!!!

The dimensions of a lawn shaped like a trapezoid are given in meters.
What is the area of the lawn in square meters? Show your work and explain your answer.

Answers

Answer:

its 43 but to show work use the reference sheet to find the formula for trapezoid

The ratio of boys and girls riding the bus is 4:3 if there are a total of 56 students on the bus,how many girls are on the bus

Answers

Answer:

18 or 14

Step-by-step explanation:

also, can u help me with my recent questin

Please help me I beg. :)​

Answers

Answer:

A and D are correct

Answer:

A and D

Step-by-step explanation:

Basically, having in mind that the earth is a sphere and the sunlights have the same length, the poles are more distant from the sunlights than the lower parts.

Please help ASAP I’m really confused please help!!!

Answers

Answer:

top right pls give brainliest

Step-by-step explanation:

what is the 3rd root of -125

Answers

Answer:

-5

Step-by-step explanation:

-5


dkfnfjdksknfmdmcnc

Pythagorean Theorem Word Problems Mazel​

Answers

Is there supposed to be a picture here?? There isn’t.

which of the following statements describe the system ?​

Answers

Answer:

one solution

Step-by-step explanation:

here, we want to select the correct option

From the system, we have two values of y

Equating the y-values

3x + 2 = -2x - 1

What this mean is that there is only a particular point where this solution will work and as such, the system has one solution

What is this anyone ??

Answers

Answer:

3.3 × [tex]10^{9}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

3300000000

Step-by-step explanation:

3 × 10^4=30000

1.1 × 10^5=110000

30000×110000=3300000000

=3300000000

Which expression is undefined? A. -8 divided by -8 B. -8 divided by 8 C. 0 divided by 8 D. 8 divided by 0

Answers

Answer:

I'll go with A

Step-by-step explanation:

well -8 got no divisor so yeah

Answer:

The answer is D

Step-by-step explanation:

8 divided by 0 = undefined

please answer with steps

Answers

Answer:

both of these.will be solved by angle sum property which states that sum of all interior angles is 180 degrees

in a

one angle is 30 degrees

other is right angle means 90 degrees

total sum of these angles is 120

total sum of all angle must be 180 degrees

so the third angle is 60 degrees

in b

one angle is 45 degrees

other is a right angle means 90 degrees

total sum of these angles is 135

total sum of all angles must be 180 degrees

so the third angle is 45 degrees

hope this helps

have a good day

thanks for points

PLEESE HELP
If someone who is 5 feet tall uses a potato gun to shoot a potato in the air at 100 feet per second, we can use the function ℎ()=−162+100+5 to calculate how far the potato will be from the ground at any given second (t).



What is the value of h(1)?

Answers

Answer:

267

Step-by-step explanation:

The cook at a local restaurant makes a special raspberry iced tea. He uses 8 small containers of the rasberry tea base to make 2 quarts of iced tea. How many small containers of the tea base will he need to make 12 quarts of the iced tea

Answers

Answer: 48 small containers

Step-by-step explanation:

Let the amount of small containers of the tea base that he will need to make 12 quarts of the iced tea be represented by x.

The information given can be formed into an expression as:

8/x = 2/12

Cross multiply

2 × x = 8 × 12

2x = 96

x = 96/2

x = 48

Therefore, 48 small containers will be needed.

I NEED HELP ASAP BEFORE MARCH 26th
Find the Value of X

Answers

Answer:

45

Step-by-step explanation:

90+45=135 180-135 is 45

HELP IM LITTTEAKAY BEGGING YALL

Answers

Answer:

The model shows a total of 2 wholes, 13 tenths and 6 hundreths. After regrouping 10 tenths into 1 whole there are 3 wholes, 3 tenths, and 6 hundredths. Therefore the sum of the numbers is 3.36

Step-by-step explanation:

J is 25 more than 3
what does j equal.

Answers


J would equal 28 because 28 is 25 more than 3. Although worded differently, all you have to do is add 3 and 25.

Answer:

jjlllllllllllslllllekkkkkkkkkkkkkkkkkkkkksnnnnnnnnnngllllljkkk

Step-by-step explanation:

kkkkkkkdkkkkkxuuuuusgggggggawwwwwwkpppgyyyyyfgggklllllllf

PLSS HELP ME ASAP I WILL EVEN GIVE U BRAINLYEST BUT PLAA HELP ME!!

Is the probability of red a simple event, complement of a
simple event, or neither?
A. complement of a simple event
B. nelther
C. simple event

Answers

Answer:

Complement of an Event: All outcomes that are NOT the event. So the Complement of an event is all the other outcomes (not the ones we want). And together the Event and its Complement make all possible outcomes.

Please helppp
a. what's the domain of c

Answers

Answer:

5

Step-by-step explanation:

I NEED HELP ASAP.
THIS IS IN SPANISH.
CAN SOMEONE TELL ME THE DIFFERENCE!!
Triángulo equilátero
Triángulo isosceles
Triángulo escaleno

Answers

Triángulo equilátero = todos los 3 lados son congruentes ("equilátero" = lados iguales)

Triángulo isósceles = solo 2 lados son congruentes

Triángulo escaleno = todos los lados son diferentes

El triángulo que se muestra aquí es isósceles porque 2 de los lados tienen la misma longitud de 7 cm.

Which best describes the probability of the rolling a 7 on a number cube that is numbered from 1 through 6

Answers

Answer:

[tex]\huge\boxed{\text{Impossible}}[/tex]

Step-by-step explanation:

To find the probability of something happening, we find all the outcomes that can happen, find all the outcomes in which our criteria is met, and set that up as a fraction, where it's criteria met/total possible outcomes.

When we roll a 6-sided die, we will have 6 possible outcomes that we can roll.

1, 2, 3, 4, 5, and 6.

We can not roll anything except these 6! Since a die only has 6 sides, numbered 1-6, we will only roll these numbers.

7 is not in this list! It is impossible to roll a 7 on a die that only has 6 sides. Since 7 isn't even possible, it would be impossible to get a 7 on a 6-sided die.

Hope this helped!

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