Is it possible for a sixth degree polynomial function with integer coefficients to have no real zeroes? Choose all that apply: Yes No

Answers

Answer 1

Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382


Related Questions

A parallelogram has and area of 37.72 m2 and a height of 4.6 m. How long is the base of the parallelogram?

Answers

Answer:

It acually equals 8.2

Step-by-step explanation:

37.72÷4.6=8.2 8.2*4.6=37.72

Hope this helps!

Two-thirds of a number increased by 3 is 11. What is the number?

Answers

2/3x + 3 = 11
subtract 3 from both sides
2/3x = 8
divide both sides by 2/3 or multiply by its inverse 3/2 to get x by itself.
x = 12

ends of a diameter: (-11, -9) and (1, -3) whats the radius and center

Answers

well, we know the endpoints of its diameter, so hmmm its center will be the midpoint of those endpoints.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-11}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 -11}{2}~~~ ,~~~ \cfrac{ -3 -9}{2} \right)\implies \left( \cfrac{-10}{2}~~,~~\cfrac{-12}{2} \right)\implies \stackrel{center}{(-5~~,~~-6)}[/tex]

well, to get its radius, we can simply get the distance between both points and keeping in mind that the radius is half the diameter, we'll take half of that distance.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-11}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-11)]^2 + [-3 - (-9)]^2}\implies d=\sqrt{(1+11)^2+(-3+9)^2} \\\\\\ d=\sqrt{12^2 + 6^2}\implies d=\sqrt{180}\implies d=6\sqrt{5}~\hfill \underset{half~that}{\stackrel{radius}{3\sqrt{5}}}[/tex]

how many terms are in each factor of this expression?
5(6 + 4x)

Answers

Answer:

2 terms

Explanation:

[tex]\dashrightarrow \ \ \sf 5(6 + 4x)[/tex]

[tex]\dashrightarrow \ \ \sf 5(6) + 5(4x)[/tex]

[tex]\dashrightarrow \ \ \sf 30 + 20x[/tex]

"x" is one term and "30" which is a constant is another term.

→ There are total two terms in this factor.

Answer:

2 Terms

Step-by-step explanation:

There will be two terms ..

=> 5(6 + 4x)

=> 30 + 20x

The Farmer Supply is building storage building for fertilizer shaped top. The that has cylindrica base and cone county laws say that the storage building must have maximum maximum height of 14 feet. Width of 8 feet and trucks deliver fertilizer in loads that are feet tall; feet wide, and 12 feet long_ Farmer Supply Dump wants t0 be able to store dump-truck loads of fertilizer: and height of the cone, h2 that Farmer Supply should use in Determine height of the cylinder; h1 will be able to store at least two dump-truck loads of fertilizer: the design: Show that your design Enter your answer and your work in the space provided

Answers

Assuming  ℎ1 = 11 feet and ℎ 2 = 3 feet, the storage of the facility is going to be 603 cubic feet, which is more than 576 cubic feet

The diameter of the building has been given as 8cm

radius = d/2 = 8/2 = 4

Maximum height = h1 + h2 = 14

Find the volume of the fertilizer that is containeed in both of the trucks

2(12x4x6) = 576 feet

From the height of 14 feets we have to assume

h1 = 11 ft,

h2 = 3 ft

How to solve for volume

[tex]volume =\frac{1}{3} \pi r^{2} h2 + \pi r^{2} h1[/tex]

= 0.333*3.14*4²*3 + 3.14*4²*11

= 602.8 ft ≈ 603

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determine the sum by suitable arrangement
i)157+376+413+524 thank you

Answers

Answer:

the answer is 1470

Step-by-step explanation:

157+376+413+524

=1470

What is the measure of side opposite to 45 degree if the side opposite to 90 degree is 4

Answers

Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

if the given figure is triangle, then the required length can be calculated:

[tex]\frac{4}{\sqrt{2} } =2\sqrt{2}.[/tex]

additional info: sin45°=1/√2.

A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now?

Answers

Answer

12 feet high

Step-by-step explanation:

A train traveling at 40 mph can go 15 more miles in the same amount of time that a car can traveling at 30 mph can go. How far does the train go in the same amount of time?

Answers

Answer:

60

Step-by-step explanation:

After 1.5 hour the train travel 60 mille (1.5 × 40) and the car travel 45 (1.5 × 30) which make the train travel 15 more than the car at the same amount of time.

Daniel used 4 strawberries and 12 blueberries to make a parfait. What was the ratio of the number of strawberries to the number of blueberries in the parfait?

A- 1:2
B- 1:3
C- 1:4
D- 1:6​

Answers

Answer:

C- 1:3

Step-by-step explanation:

You have to simply 4 and 12, which becomes 1 and 3 (by dividing both numbers by 4). Then I guess you just keep a colon symbol in between 1 and 3.

A line passes through the point (-10, -8) and has a slope of -1/2. Write an equation in slope intercept form for this line

Answers

Start with the slope intercept formula.

y = mx + b

Plug in the slope and coordinates for x and y and solve for b (y-intercept)

-8 = -1/2(-10) + b
-8 = 5 + b
-13 = b

Then rewrite the equation in slope intercept form

y = -1/2 x - 13

PLEASE CHOSE THE RIGHT ANSWER AND EXPLAIN WHY YOU CHOSE IT PLEASE

Answers

Answer:

D

Step-by-step explanation:

See attached image.

Find the value of csc 0 if cos 0 = -3/5 and 0 is in the second quadrant.

Answers

we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill[/tex]

If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?
1/5
4/5
5
16

Answers

Answer:

Step-by-step explanation:

y = k*x                    This is the formula for a direct variation.

y = 20x = 4                        Substitute these values into the direct variation

20 = 4 * k                        Divide by 4

20/4 = 4k/4

k = 5

Answer: the constant of variation is 5

help me out on this problem

Answers

75 minutes because 4 x 2 = 8 which means you need to do 30 x 2 which equals 60. We know 2 miles will be ran in 15 minutes so when we add these we get 10 miles in 75 minutes.

What is the measure of ZRST?
R
46
T
O A. 46°
O B. 92°
O .
C. 23°
D. 44°
s

Answers

Answer:

ОА. 449

ОВ. 23°

Ос. 92°

OD. 46°

Step-by-step explanation:

The measure of the angle RST is 23 degrees, option C is correct.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that an arc is 46∘

We need to find the measure of the subtending angle inscribed in the circle.

The measure of the angle inscribed in a circle is one-half the measure of the arc it subtends.

The measure of the arc is twice the measure of the subtending inscribed angles.

measure of the angle RST= 1/2 measure of the arc

∠RST=1/2(46)

=23 degrees.

Hence, the measure of the angle RST is 23 degrees, option C is correct.

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#SPJ7

Who ran at a faster constant rate and which equation represents the relationship between Paul's distance and his time

A = Paul ran at a slower constant speed than Melinda, y=1x x being time in hours y being the distance in miles Paul ran

B = Paul ran at a slower constant speed than Melinda, y =3x x being time in hours, y being distance in miles Paul ran

C = Paul ran at a faster constant speed than melinda, y =5x where x is the time in hours and y is the distance in miles Paul ran

D = Paul ran at a faster constant speed than melinda, y =7x x being time in hours and y is the distance in miles Paul ran

Answers

Given the proportional relationship representing the speed, Paul ran faster. The equation for Paul is, y = 7x (Option D).

What is the Equation of a Proportional Relationship?

Proportional relationship between two variables that has a constant rate or unit rate of m, is given as y = mx.

In a graph, the steeper the slope, the larger the constant rate or unit rate.

The graph for Paul is steeper than that of Melinda. Since Melinda's constant speed is 5, therefore, Paul's constant speed cannot be less than 5. It should be more than 5, i.e. 7.

This means that Paul ran at a faster constant speed than Melinda did.

Paul's equation for distance covered over time can be expressed as, y = 7x. (Option D).

Learn more about proprotional relationship on:

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Please help with this easy math problem. Due soon.

Answers

Answer:

Step-by-step explanation:

Exponential equation:

           [tex]\boxed{y=a*b^{x}}[/tex]

Choose the point whose x-coordiante is 0, so that we can find the value of a.  (0,2)

[tex]2 = a*b^0\\\\2 = a*1 \ [\text{\bf any \ variable raised to 0 is 1}][/tex]

[tex]\sf \boxed{a = 2}[/tex]

Now, choose (1 , 1) and find the value of b

[tex]1 = 2*b^{1}\\\\1 = 2*b\\\\\dfrac{1}{2}=b[/tex]

Exponential equation:

            [tex]\bf \boxed{y =2* \left(\dfrac{1}{2}\right)^{x}}[/tex]

Ramon and Hector ride their bikes at constant rates during a race. Ramon rides 45 miles in 3 hours. The distance, y, in miles, Hector rides in x hours is given by the equation y = 18x. Which statement is true?
No answer text provided.

No answer text provided.

Ramon rides his bike 3 miles per hour faster than Hector rides his bike.

Ramon rides his bike 27 miles per hour faster than Hector rides his bike.

Ramon rides his bike 3 miles per hour slower than Hector rides his bike.

Ramon rides his bike 27 miles per hour slower than Hector rides his bike.

Answers

We will find the speeds of both persons, the correct option is:

"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."

Which statement is correct?

First, we know that Ramon rides 45 miles in 3 hours, then its speed is:

S = 45mi/3h = 15mi/h

And we know that Hector position is given by:

y = 18x

Where x is time in hours, so his velocity is 18mi/h.

Then we can see that:

Ramon's speed = 15mi/hHector's speed = 18mi/h

So the correct statement is:

"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."

If you want to learn more about speed, you can read:

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its 8th grade math super easy

Answers

[tex] {15}^{2} + {x}^{2} = {39}^{2} [/tex]

x = 36

^● ●^

Answer:

36

Step-by-step explanation:

You can use Pythagorus to solve this. 39^2-15^2=1296. √1296 is 36

Where is the removable discontinuity of f (x) = startfraction x 5 over x squared 3 x minus 10 endfraction located? x = –5 x = –2 x = 2 x = 5

Answers

The removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).

What are discontinuities?

Holes in the graph of function, where its undefined, or non-continuous, is called discontinuity.

The points in the domain of the function over which its not continuous, is called point of discontinuity for that function.

What is removable discontinuity?

A discontinuity is removable if the limit of the function at the point of discontinuity exists but this limiting value is not the value of the function at that point.

We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.

The given function is:

[tex]f(x) = \dfrac{(x+5)}{(x^2 +3x-10)}[/tex]

Factoring the denominator, we get:

[tex]x^2 + 3x -10 = x^2 + 5x - 2x - 10 =x(x+5) - 2(x+5) = (x+5)(x-2)[/tex]

Therefore, we get:

[tex]f(x) = \dfrac{(x+5)}{(x+5)(x-2)}[/tex]

The function is not defined if x = -5, or x = 2 since at those places, the denominator would become 0. (we cannot cancel out (x+5) from numerator and denominator for all x, as it isn't defined for x = -5

Also, we have:

[tex]\lim_{x\rightarrow 2}f(x)= \infty\\\lim_{x\rightarrow -5}f(x) = \lim_{x\rightarrow -5}\dfrac{(x+5)}{(x+5)(x-2)} = \lim_{x\rightarrow -5}\dfrac{1}{(x-2)} = -\dfrac{1}{7}[/tex]

We cancelled out (x+5) from numerator and denominator because x is limiting to -5 but isn't equal to -5.

For discontinuity of x = -5, the limit of f(x) exist (left and right limit both will come as 1/3). But f(-5) is not defined. So we can remove this discontinuity by defining f(-5) = 1/3 and for rest of the values of x, it is same as before.

Thus, the removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).

Learn more about discontinuities here:

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Answer: Option A  -5

Step-by-step explanation: Just took the test

What number when multiplied by itself is 11 greater.

Answers

Answer:

6

Step-by-step explanation:

Josh has a rewards card for a movie theater.
• He receives 15 points for becoming a rewards card holder.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 55 points to earn a free movie ticket.
Which inequality can Josh use to determine x, the minimum number of visits he needs
to earn his first free movie ticket?

PLSS HELPPPP =((( plss

Answers

Answer:

55 ≤ 3.5x + 15

Step-by-step explanation:

Missing Inequality.

Given that:

Josh has a reward card for movie theater.

He receives 15 points for becoming a rewards card holder.

He earns 3.5 points for each visit to the movie theater.

He needs at least 55 points to earn a free movie ticket.

To Find:

Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?

Solution:

From the given we know that:

Points Josh received for becoming a member = 15

Points Josh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

Note that:

< = Less than

> = Greater than

≤ = Less than or equal to

≥ = Greater than or equal to

Thus, We know that Josh need to get less than or equal to 55.

Therefore, we use this sign ≤

Since we know that we need to get less than or equal to 55 then

we get

55 ≤ 3.5x + 15.

Hence, the inequality that Josh can use to determine x, the minimum number of visits he needs to earn his first free movie tickets is:

55 ≤ 3.5x + 15

Kavinsky

PLS HELP

No links pls and Ty <33!!!

Answers

Answer:

C = 2πr = 2·π·20 ≈ 40π ft (125.6)

Lin goal is to drink 8 cups of water every day she drags 37 oz of for lunch today how much more water does Linda need to drink today to reach her goal

Answers

Answer: 27

Step-by-step explanation:

8 cups of water is 64 Ounce. If she had 37, She needs 64 - 37 To balance up

>>>>>>>>>>>>>>>>>>>>

Answers

Answer:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

<<<<<<<<<<<<<<<<<<<<

hope it helps...!!!

Derek saves 10% of his paycheck each week to buy a mountain bike the mountain bike costs 340.00 Derek receives a paycheck in the amount of $280.50 each week how many paychecks will Derek have to receive before he has saved enough money to buy the mountain bike

Answers

Answer: 13 weeks

Step-by-step explanation:

First you have to find 10% of 340.00 which is 28, so each week he saves 28.00 for his bike. To find how many paychecks he has to recieve you divide 340.00 by 28.00, which is 12.1, since there is a decimal place you have to round it up to 13 because it is a little bit more than 12 paychecks. ;)

What are the coordinates of point B' after
AABC is reflected across the y-axis?
5 y
А
В'
?
?
с
B (3,2
-5
0
-5

Answers

Answer:

B'(-3, 2)

Step-by-step explanation:

The rule for a reflection over the y-axis is (x, y) → (-x, y)

This means that the x-values change while the y-values stay the same.

B(x, y) → (-x, y)

B(3, 2) → (-3, 2)

B'(-3, 2)

Hope this helps!

The school auditorium has 448 seats arranges in 32 equal rows. How many seats are in each row?

Answers

14
448 total/32rows=14 seats in each row

True or false? If you took a true "il then statement and revered the clauses,
the new statement would also be true
O A True
O B. False

Answers

the answer to ur question is false

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