According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
ORX)-(3x? -x-5)(2x-5
1 x) = (3x* +2x)"
o 9x)= (4x2-7)
OM) - Bx - 4y - 1) (3,2-4

According To The Fundamental Theorem Of Algebra, Which Polynomial Function Has Exactly 8 Roots?ORX)-(3x?

Answers

Answer 1
Answer: Choice A

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Explanation:

For each expression in the parenthesis of choice A, focus only on the leading terms. Those would be the terms to the very left. The leading terms 3x^2 and 2x^6 multiply to 6x^8. This is the leading term of the final expansion and it's of degree 8. Any degree 8 polynomial will have 8 roots according to the fundamental theorem of algebra. Some of those roots may be complex numbers, or they may be purely real numbers.

Choice B can be ruled out because the leading term 3x^4 is raised to the 4th power to get (3x^4)^4 = 81x^16 as the leading term of the final expansion. This polynomial has 16 roots, but we want 8 roots instead.

Choice C is a similar story to choice B. In this case, we have (4x^2)^3 = 64x^6 as the leading term when you expand everything out. This 6th degree polynomial has 6 roots.

And finally, choice D can be ruled out as well. We follow the same steps as choice A. The leading terms from each parenthesis group multiply to 6x^8*3x^2 = 18x^10 showing we have 10 roots (due to the 10th degree polynomial).


Related Questions

Claire's music playlist contains songs she bought and songs her mother bought. The ratio of her songs to her mother's songs is 3:2. Which table shows this ratio and two equivalent ratios?​

Answers

Answer:

B.

Step-by-step explanation:

The ratio of Claire's songs to her mother's songs = 3 : 2

A.

3 : 2 = 3/2

9 : 6 = 9/6 = 3/2

12 : 10 = 12/10 = 6/5

B.

3 : 2 = 3/2

6 : 4 = 6/4 = 3/2

15 : 10 = 15/10 = 3/2

C.

3 : 2 = 3/2

4 : 3 = 4/3

5 : 4 = 5/4

D.

3 : 2 = 3/2

4 : 6 = 4/6 = 2/3

20 : 30 = 20/30 = 2/3

The table which shows the correct ratio and two equivalent ratios is B

Somebody help i need to find the value of x and classify the sides and angles

Answers

Answer:

a) x=18

b) 36 (2*18)

c) 54 (3*18)

d) I'm not exactly sure what it's asking for, so I don't know

Step-by-step explanation:

triangle sum theorem means the sum of every triangle is 180 degrees

so we can make this equation: 180 = 90 + 2x + 3x

solve and you get 18.

what is the volume of the following rectangular prism 9/5 units 2/3 units ​

Answers

Answer:

1.2

Step-by-step explanation:

9/5*2/3=1.2

Find the circumference

Answers

Answer:

75.36 mi

Step-by-step explanation:

Given :-

Radius = 12 mi .

We know :-

→ Circumference = 2 π r

→ C = 2 * 3.14 * 12 mi

C = 75.36 mi

Answer:

Step-by-step explanation:

circumference of a circle=2πr

=2*3.14*12

=24*3.14

=75.36 mi

HELPP!!!!!x
And thanks!

Answers

Answer:

7/10 > 17/25

Step-by-step explanation:

17/25  and 7/10

The common denominator is 50

17/25 *2/2 =34/50

7/10 *5/5 = 35/50

35 > 34 so

35/50 > 34/50

7/10 > 17/25

which expression is equivalent to 1/2r + 8p - 3/4r -2p
A. 1/4r -6p
B. 1/4r +10p
C. 1/4r + 10p
D. 5/4r + 6p​

Answers

Answer:

D.5/4r+6p

Step-by-step explanation:

hula kong hahha

Can someone tell me which one it is?

Answers

Answer:

-16

Step-by-step explanation:

-16... using d = b²-4ac

Answer:

the discriminant is –16

hope this helps!

Shelly purchased 6 25'-tape
measures and 2 chalk line reels for
$78. Sean purchased one 25'-tape
measure and 3 chalk line reels from
the same store for $29. What was
the price of each 25'-tape measure
and each chalk line reel?

Answers

Answer:

Price of one 25'-tape measure = $11

Price of one chalk line reels = $6

Step-by-step explanation:

Let t = price of one 25'-tape measure, and

let c = price of one chalk line reel

"Shelly purchased 6 25'-tape measures and 2 chalk line reels for $78."

6t + 2c = 78

"Sean purchased one 25'-tape measure and 3 chalk line reels ... for $29."

t + 3c = 29

We have a system of two equations in two variables. We will solve it with teh substitution method.

Solve the second equation for t.

t = 29 - 3c

Substitute 29 - 3c for t in the first equation.

6(29 - 3c) + 2c = 78

174 - 18c + 2c = 78

-16c = -96

c = 6

Substitute 6 for c in the second original equation.

t + 3(6) = 29

t + 18 = 29

t = 11

Answer:

Price of one 25'-tape measure = $11

Price of one chalk line reel = $6

Amelia is taking a road trip. She drove 250 miles the first day. If 250 is 40% of her total distance, how many miles is her roadtrip in all?

Answers

Answer: 625 miles

Step-by-step explanation:

100-40=60

so she has 60% for her distance so lets munis 40 from it and add 250 to 250

250+250=500

60-40=20

20 is half of 40 so whats half of 250? its 125

so she drove 625 miles for her road trip 2 and 1/2 a day

Find the circumference of a circle with diameter,
d
= 3.2m.
Give your answer rounded to 2 DP.

Answers

Answer:

[tex]circumference = \pi \: d \\ = 3.14 \times 3.2 \\ = 10.05 \: m[/tex]

Answer:

circumference=10.05 m

Step-by-step explanation:

radius =diameter/2

=3.2/2

=1.6 m

circumference=2πr

=2*3.14*1.6

=10.048 m

=10.05 m

Which sequences are geometric? Check all that apply.

Answers

Step-by-step explanation:

A geometric sequence is when we multiply one number by a set rate to obtain the next number.

For the first one, we multiply 5 by 2 to get 10, 10 by 2 to get 20, and so on. This is geometric

Next, we multiply 3 by 4 to get 12, 12 by 4 to get 48, and so on. This is geometric

Next, we multiply 3 by 5 to get 15, 15 by 5 to get 75, and so on. This is geometric

Next, we multiply 8 by 15/8 to get 15, and 15 by 5 to get 75. 15/8 and 5 are not the same so this is not geometric

Next, we multiply 14 by 21/14 to get 21, and 21 by 28/21 to get 28. 21/14 and 28/21 are not the same so this is not geometric

Next, we multiply 17 by 20/17 to get 20, and 20 by 23/20 to get 23. 20/17 and 23/20 are not the same so this is not geometric.

Finally, we multiply 2 by 5 to get 10, 10 by 5 to get 50, and so on. This is geometric

for the same girl again plz.

Answers

Answer:

Option A is correct

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

Hope it is helpful...

Can pls someone help I need help

Answers

a^2 + b^2 = c^2
9^2 + b^2 = 15^2
81 + b^2 = 225
225 - 81 = b^2
144 = b^2
square root of 144 = 12
b = 12

Subtract: (-137° + 6) - (-43°) Your answer should be in simplest terms. Enter the correct answer.​

Answers

Answer:

-9y⁹ + 6

Step-by-step explanation:

Subtracting a negative makes it positive

-13y⁹ + 6 + 4y⁹

combine like terms

-9y⁹ + 6

What is 2x^2(x-5) divided by 10x when x + 10?

Answers

Answer:

1000

Step-by-step explanation:

2x²(x - 5) ÷ 10x

x = 10

2(10)²(10 - 5) ÷ 10(10)

20²(5) ÷ 100

100² ÷ 100

100000 ÷ 100

1000

How many four-digit integers contain only the digits 1, 2, 3, 4, and 5, with the property that no two consecutive digits are the same?

Answers

Answer:

120

Step-by-step explanation:

we solve this question by using permutation because the order matters

nPr

5P4 = 120

14 is what % of 89 if you choose a random answer you will be reported

Answers

Answer:

15.73 %

Step-by-step explanation:

Given :-

14 is what % of 89 .

For finding% :-

→ 14/89 * 100

15.73 %

Answer:

15.73% to the nearest hundredth.

Step-by-step explanation:

14/89 = 0.157303

Now multiply  by 100

This gives 15.7303 %

What’s a converse in mathematics

Answers

Answer:

A converse is the result of reversing its two constituent statements.

Example, P-Q. Converse would be Q-P

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. ... Either way, the truth of the converse is generally independent from that of the original statement.

A• 3.7

B• 3.8

C• 5.3

D• 5.4

Answers

Answer:

D 5.4

Step-by-step explanation:

The pythagoras theorem states that a² + b² = c²

2² + 5² = ?²

4 + 25 = ?²

29=?²

? =

[tex] \sqrt{29} [/tex]

? = 5.4 rounded 2 sig fig one decimal place

(04.02 MC)
4
What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)?

Answers

Answer:

The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.

Step-by-step explanation:

The line [tex]y = x + 1[/tex] has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:

[tex]m_{\perp} = -\frac{1}{m}[/tex] (1)

Where:

[tex]m[/tex] - Slope of the original line.

[tex]m_{\perp}[/tex] - Slope of the line perpendicular to the original line.

If we know that [tex]m = 1[/tex], then the new slope is:

[tex]m_{\perp} = -\frac{1}{1}[/tex]

[tex]m_{\perp} = -1[/tex]

A line is defined by the following expression:

[tex]y = m\cdot x + b[/tex] (2)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]m[/tex] - Slope.

[tex]b[/tex] - Intercept.

If we know that [tex](x,y) = (4,1)[/tex] and [tex]m = -1[/tex], then the intercept of the line perpendicular to the original line:

[tex]b = y - m\cdot x[/tex]

[tex]b = 1+4[/tex]

[tex]b = 5[/tex]

The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.

Lee ran a mile in 7 1/3 minutes. His friend Sam ran the same mile in 8 5/9 minutes. How many minutes faster did Lee run? (First answer will be the brainliest)

Answers

He ran the mile 1 and 3/9 minutes faster

Alex accepted a job as a veterinarian that pays a salary of $78,500 in the first year. After the first year, his salary increased by 1.5% per year.

Alex works for the vet clinic for 10 years. What is the total of his earnings over the 10 years?

Round your answer to the nearest hundredth

$ = _______

Answers

Answer:

795.597,5

Step-by-step explanation:

let's consider the fact that Alex worked for the vet for 10 years. First year is off with $78,500 since that was his first payment, now there are nine years left. With some math operations we find that 1,5% in this problem is equal to 1.177,5$. So if we take that number and put it together with Alexs' first payment we get from now and on his yearly pay, which is $79.677,5. At last we take that number multiply it by 9 and add all the numbers together (78,500+79.677,5(×9)= 795.597,5)

The total of his earnings over the 10 years is $236677.5.

What is interest rate?

The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time.

Given

P = $78,500

Interest rate = 1.5 %

Time t = 10 years

Total earning = P[tex](1+\frac{r}{100} )^{t}[/tex]

A = 78500[tex](1+\frac{1.5}{100} )^{t}[/tex]

A = 78500[tex](\frac{1015}{100} )^{10}[/tex]

A = 78500[tex](\frac{230}{200} )^{10}[/tex]

A = $236677.5

Hence, the total of his earnings over the 10 years is $236677.5.

Find out more information about interest rate here

https://brainly.com/question/7279636

#SPJ2

Complete the point-slope equation of the line through (-8,-8)(−8,−8)left parenthesis, minus, 8, comma, minus, 8, right parenthesis and (-7,9)(−7,9)left parenthesis, minus, 7, comma, 9, right parenthesis.
Use exact numbers.
y-9=y−9=y, minus, 9, equals

Answers

Answer:

[tex]y-9=17(x+7)[/tex]

Step-by-step explanation:

Hi there!

What we know:

The line goes through the points (-8,-8) and (-7,9)We need to write the equation of the line in point-slope form

What we need to know:

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that the line passes throughWe're given "[tex]y-9=[/tex]", which is the "[tex]y-y_1[/tex]" part of the point-slope form equation. This means that [tex](x_1,y_1)[/tex] is [tex](-7,9)[/tex] and we only need to solve for m.

Our equation so far (plugging in the point (-7,9):

[tex]y-9=m(x-(-7))[/tex]

[tex]y-9=m(x+7)[/tex]

Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-8,-8) and (-7,9)

[tex]=\frac{-8-9}{-8-(-7)}\\=\frac{-8-9}{-8+7}\\=\frac{-17}{-1}\\= 17[/tex]

Therefore, the slope of the line is 17. Plug this into [tex]y-9=m(x+7)[/tex]:

[tex]y-9=17(x+7)[/tex]

I hope this helps!

can someone help please.

Answers

Answer:

if im not mistaken is d hope you get it right

How many liters are equivalent to 25 ml​

Answers

Answer:

0.025 liters

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

0.025 liters

Step-by-step explanation:

asma is drawing a picture of a tree.she drawss a 15m tree as 3cm in her drawing book. if a fruit acctualy hangs from branch 3 m from the ground how high must asma draw it to keep the proportion correct?

Answers

Answer:

0.6 cm

Step-by-step explanation:

she divided the the height of the tree 500, so the same factor has to be applied to everything else

3m * 1/500 = 0.6cm

simplify 26a+4a-10a​

Answers

Answer:

20a

Step-by-step explanation:

26a+4a-10a=30a-10a=20a

Answer:

20a

Step-by-step explanation:

26a+4a-10a

since they are like terms u can add and subtract them

=30a-10a

=20a

PLEASE HELP!!!!!!!!!!!!!

Answers

Answer: I think E

Step-by-step explanation:

can someone help with part A please??

Answers

Answer:

Step-by-step explanation:

4 days 9 hours 40 minutes

HELP ASAP- IF YOU ARE CORRECT I WILL MARK BRAINLY

Answers

The Answer is:

B) -3/2

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