Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1 − √6, 1+ √6, and 5-i
(Simplify your answer)

Answers

Answer 1

What is polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..

This leads to a polynomial of ...

p(x) = (x - 5)(x - (4+i))(x - (4-i))

Now we can simplify...

(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17

Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...

p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85

So p(x) = x3 + 3x2 + 57x - 85

p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested

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Related Questions

Haley borrows 1000 dollars from her bank.She will pay the loan at a simple annual interest rate of 4% over 4 years.How much will she pay back altogether

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Answer: $49.85

No explanation needed

Find the length of side X in simplest radical form with a rational denominator.
X

Answers

Answer:

given in the figure an isosceles right triangle

hence

x = √3

√3 is a surd it can't be simplified further

A class collects data on the number of movie tickets purchased and total cost of those tickets. The class plots the data on a scatter plot. Which statement best interprets their results

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Answer:

what are your options?

Step-by-step explanation:

Help I’ll give Brainly est

Answers

Answer:

60 square centimeters

Step-by-step explanation:

8*15/2 = 60

Answer:

Ugh A bad B but C and D seem correct to fit in into your own a jar of yellow

hello help please i’ll give brainliest

Answers

Answer:

Erosion by groundwater.

Step-by-step explanation:

Sinkholes are formed when groundwater dissolves rocks underneath the land surface.

Answer:

Erosion of groundwater because the water goes through the rock and "weekends" them into collapsing. Almost like tripping if you will.

Step-by-step explanation:

WILL GIVE BRAINLIEST!!!!
Priscilla received 240 votes in the election for student council president. That was 60% of the students who voted in the election. How many students voted in the election? *

A) 400 students
B) 300 students
C) 185 students
D) 455 students

Answers

It’s “A” 60% of 400 students

Answer:

I think its c

!

Step-by-step explanation:

Michael is buying new tile for his bathroom. The bathroom is 6 feet wide and 7 feet long. It costs $1.75 per square foot of material for the bathroom. If Michael goes to the store with $70, will he have enough money to buy the material. Why or why not.

Answers

Answer: yes because  all the math adds up to 22.75 and he has 70

Step-by-step explanation:

An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest circle that could fit in the square, like the drawing above.
How many more inches of silver wire did the artist use compared to copper wire? (remember that = 3.14)

Answers

Answer:

1.4 inches

Step-by-step explanation:

if I'm wrong please tell me right away I would like to help you good day.


These two polygons are similar.
4
2
9
16
15
w
w = [? ]


45 points asap for anyone who can answer

Answers

6/2=3
The scale factor is 3
3x3=9
w=9

Find mDE. Round your answer to the nearest hundredth.

Answers

Answer:

[tex]50.04[/tex]

Step-by-step explanation:

Use this formula for arc length

[tex]2\pi \times r( \frac{x}{360} )[/tex]

where r is the radius and x is the arc measure.

We know Arc de is 8.73 so we are finding x.

R equal 10.

[tex]2\pi \times 10( \frac{x}{360} ) = 8.73[/tex]

[tex]20\pi( \frac{x}{360} ) = 8.73[/tex]

[tex]20\pi \times x = 3142.8[/tex]

[tex]x = \frac{3142.8}{20\pi} [/tex]

x=50.04

The value of the angle will be 50.04.

What will be the angle?

It is given in the question that

The arc of the circle A=8.73 In

The radius of the circle =10 In

Now from the formula of arc

[tex]A=2\pi r(\dfrac{\theta}{360} )[/tex]

[tex]8.73=2\pi 10\times \dfrac{\theta }{360}[/tex]

[tex]\theta = \dfrac{8.73\times 360 }{ 2\pi\times 10} =50.04[/tex]

[tex]\theta=50.04[/tex]

Thus the value of the angle will  be 50.04

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Factor 5/6 out of 5/6z+15

Answers

Answer:

5/6z+15

heart if it helped!

Help, I am unsure about what to do exactly

Answers

You plug in number for number getting 194.8 which is equal to 2931

Solve for x. Give explanation

Answers

Answer:

x =  47 degrees.

Step-by-step explanation:

The angles in a triangle add up to 180 degrees, therefore:

x + 43 + 90 = 180

x = 180 - 43 - 90

x = 180 - 133

= 47 degrees.

what equation is equal to y-34=x(x-12)

Answers

Answer: I don’t know how to solve for x but I know how to solve y for y=x^2-12x+34

Step-by-step explanation: Hope this help :D

What is 73/48 simplified

Answers

Answer:7348 is already in the simplest form. It can be written as 1.520833 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

Answer: it’s already at its lowest form

Step-by-step explanation:

Need help on this, I have no idea what should go on the first line or the second line​

Answers

Answer:

1.) 120

2.)120

Step-by-step explanation:

1.) Do length times width

2.) For the number 120 you don't have to round, so it just stays the same

Select all of the angles that are congruent to \angle 5.

Answers

Answer:

<5 = <8 b/c of vertical angles

<5 = <4 because of alternate interior angles

<5 = <1 because of corresponding angles

Which of the following systems of equations creates the graph of (-3.4, 2.3)?

Option 1 : y= 2x+4
y= -1/3x-8
Option 2 : y= 1/2x-8
y= -3x-8/3
Option 3 : y= 1/2x+4
y= -3x-8
Option 4 : y= 2x-8
y= -1/3x-8/3

I need an answer ASAP, I will mark u brainliest if the answer is valid! thx

Answers

Answer:

C

Explanation:

The answer is C because when you plug in (-3.4) as x in that equation, you get 2.3 as an answer which means that option is correct.

[tex]y = \frac{1}{2} x + 4[/tex]

[tex] = \frac{1}{2} ( - 3.4) + 4[/tex]

[tex] = 2.3[/tex]

When you plug in x for other options, you do not get the correct value for y so this is the only answer.

I need help on this test. Will give Brainliest to whoever answers first!

Answers

Answer:

C and G.

Step-by-step explanation:

Describe a real world situation where you might use the Pythagorean Theorem. Help due today :))

Answers

Answer: When carpenters want to construct a guaranteed right angle, they can make a triangle with sides 3, 4, and 5 (units). By the Pythagorean Theorem, a triangle made with these side lengths is always a right triangle, because
3^2
+
4^2
=
5^2


Explanation: hope this helps

Are the triangles congruent ? Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!

Answers

Answer:

no

Step-by-step explanation:

they are not

Answer:

No

Step-by-step explanation:

because the angles are not equal. If they were they would have the same numbers.

0.11 times 734 Answer please.

Answers

Answer:80.74

Step-by-step explanation: lol

Dannon has $10.80 in dimes and quarters. If Dannon has 32 more quarters than dimes, how many dimes does he have?

Answers

Answer:

Dannon has 8 dimes.

Step-by-step explanation:

8 dimes. by solving the system of equations

10d + 25q = 1080

q = d + 32

we find

d = 8 dimes

q = 40 quarters

what is the answer of 2m^2 * 2m^3

Answers

Answer:

4m^5

Step-by-step explanation:

Answer:

4m^5

Step-by-step explanation:

32 divided 10 - 8 divided 2 - 3

Answers

Answer:

-3.8

Step-by-step explanation:

Answer:

-3.8 i think sorry this is the first one im not sure with.

Step-by-step explanation:

32/10=2.4

3-2=1

2.4-8=5.6

5.6/1=5.6

=-3.8

How many tiles will be in figure 100? EZ COME UP ON POINTS

Answers

Answer

.

[tex]f(100) = 498[/tex]

.

Explain

.

[tex]f(2) = 8[/tex]

[tex]f(3) = 13[/tex]

.

Find b

[tex]3b - 2b = 13 - 8[/tex]

[tex]b = 5[/tex]

.

Find f(1)

[tex]f(1) = f(2) - b[/tex]

[tex]f(1) = 8 - 5[/tex]

[tex]f(1) = 3[/tex]

.

Find f(100)

[tex]f (x)= f(1) + (x - 1)b[/tex]

[tex]f(100) = 3 + (100 - 1)5[/tex]

[tex]f(100) = 3 + (99)5[/tex]

[tex]f(100) = 3 + 495[/tex]

[tex]f(100) = 498[/tex]

.

#LearnWithBrainly

10+15+6+15+5+15+7+13

Answers

Answer:

I think its 86

Step-by-step explanation:

I used a calculator.

how do i find the surface area and volume of this shape?

Answers

Answer:

3,761.46 m³

Step-by-step explanation:

Volume of a cone = 1/3πr²h

π = 3.14

radius, r = diameter/2

= 25/2 = 12.5 m

Height, h = 23m

Volume of a cone = 1/3πr²h

= 1/3 * 3.14 * 12.5² * 23

= 1/3 * 3.14 * 156.25 * 23

= 11,284.375 / 3

= 3761.4583333333

Approximately,

Volume of the cone = 3,761.46 m³

Rachel buys a bag of apples for $3.21. She pays for the bag with a $20 bill. How much change should Rachel receive?

Answers

Answer:

$16.79

Step-by-step explanation:

20 - 3.21 = 16.79

$17.79

Hope that helps :)

Need help once again!!!

Answers

Answer:

the answer to this question is seven

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