What are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 + 5x3 − x2 + 8x + 4? (1 point)

Answers

Answer 1

Answer:

Using Descartes' Rule of Signs, we observe whether each consecutive term has a + or - sign:

f(x) = 3x4 − 5x3 − x2 − 8x + 4

Signs are: + - - - +

There are 2 sign changes (from +3 to -5, then from -8 to +4). This means that there are either 2 or 0 positive roots. (We take the number of sign changes, which is 2, and subtract by 2s to get all possible numbers of positive roots.)

For negative roots, we first invert all the odd-powered terms in f(x):

3x4 + 5x3 − x2 + 8x + 4

Signs are: + + - + +

There are 2 sign changes, from +5 to -1, and from -1 to +8. Therefore, there are either 2 or 0 negative roots.

Since the overall degree of f(x) is 4, the total number of roots must sum up to 4. There are either 2 or 0 positive roots, and 2 or 0 negative roots, and everything that remains will be a complex root. The possibilities are:

2 positive, 2 negative, 0 complex

2 positive, 0 negative, 2 complex

0 positive, 2 negative, 2 complex

0 positive, 0 negative, 4 complex.

Therefore we can have either 0, 2, or 4 complex roots.

The correct answer is the last choice.


Related Questions

In order to join a yoga club you have to pay an annual fee and a fee per class. At Yoga For Us the annual fee is $30 and $5 per class. At Stretch Land the annual fee is $60 and
$2 per class. After how many classes would the fees be the same?
After 10
classes the feels the same.

Answers

It will take 10 classes for YOGA FOR US & STRETCH LAND to have the same amount of money spent on yoga classes.

For Yoga For Us after 10 classes . You would have spent 50 dollars for the classes,plus our $30 fee is (50+30) which is $80

For Stretch Land after 10 classes.  You would have spent 20 dollars for the classes,plus our $60 fee is (60+20) which is $80.

Each yoga studio will have gathered $80 after 10 classes.

Hope this helps <3 & don't forget to drink water!!

Gatorade comes in two different sizes A 16 ounce costs $2.10 and a 20nounce bottle costs $3.15 which is a better deal to explain your thinking.

How much do you save per ounce by buying the better one?

Answers

Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03

The first step is to find the cost per ounce of each bottle.

For the 16 ounce bottle:

= 2.10 / 16

= $0.13 per ounce

For the 20 ounce bottle:

= 3.15 / 20

= $0.16

The 16 ounce size is therefore better and the amount saved per ounce is:

= 0.16 - 0.13

= $0.03

In conclusion, the 16 ounce is better as it saves $0.03 per ounce.

Find out more at https://brainly.com/question/16805756.

can someone plz help me I need the answer asap ​

Answers

Answer:

no. c is the correct answer

do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.

Answers

I would think the answer is no because the x is going up times 2 (2x2=4) and the y is going up plus 1 (1+1=2)

Answer: No

Step-by-step explanation:

Given that f(x)=x-5 g(x)=5x and h(x)=-f(x+1)-3g(x-1), then what is the value of h(3)?

please show step by step answer.

Answers

Answer:

Step-by-step explanation:

f(x) = x - 5 and g(x) = 5x

- f(x + 1) = - ( x + 1 - 5 ) = 4 - x

- 3g(x - 1 ) = - 3 [ 5 (x - 1)] = 15 - 15x

h(x) = 4 - x + 15 - 15x = 19 - 16x

h(3) = 19 - 16(3) = - 29

Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?

f(x)=x^3 -5x + (2/5)

(A) 1/2
(B) 1/5
(C) 1
(D) -1

Answers

The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.

(a) 1/2 is not a possible zero of the function

The function is given as:

[tex]f(x) =x^3 - 5x + \frac 25[/tex]

For a function,

[tex]f(x) = px^n +......q[/tex]

The list of possible roots is:

[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5

[tex]5f(x) = 5x^3 - 25x + 2[/tex]

So, we have:

[tex]p= 5[/tex]

[tex]q = 2[/tex]

The factors are:

[tex]p =\pm 1, \pm 5[/tex]

[tex]q =\pm 1, \pm 2[/tex]

So, the possible roots are:

[tex]Roots = \pm\frac{1,2}{1,5}[/tex]

Split

[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]

Hence, 1/2 is not a possible zero of the function

Read more about rational zero test at:

https://brainly.com/question/12860313

Share 120 in the ratio 3:5:7

Answers

Answer:

24:40:56

Step-by-step explanation:

3+5+7=15

120/15=8 1 Ratio is 8

3x8=24

5x8=40

7X8=56

i dont know if its the easiest method

Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14

Answers

The perimeter would be

2(3n - 7) + 2(n + 5)

6n - 14 + 2n + 10

Simplify

8n - 4

So the answer would be C

I need a fast answer because I’m about to get on a plane

Answers

Answer:

C

Step-by-step explanation:

-6 is less than 7

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer:

$8.00

Step-by-step explanation:

20% of 44.85=8.97

thats the closest to 8.00

Answer:

the answer is 9 dollars cuz the real answer is $8.97 and round to the nearest whole the answer is 9

Step-by-step explanation:

Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.

How many square inches of the protective covering does she need for the case?

Answers

Answer:

336

Step-by-step explanation:

We know that a cube has 6 faces which means we can use this equation:

56 x 6 = 336

336 square inches is the answer.

Perimeter=56in

Side=56)4=14in

So area of one side=

(side)^2=(14)^2=196in^2

Cube has 6sides

So total protection:-

6(196)1176in^2

Mr. Glenn is making 30 school supply baskets. notepads come in packs of 5. Erasers come in packs of 15 and markers come in packs of 3. what is the least number of each package she should buy to have 1 item in each basket and no supplies left over

Answers

He will need 6 packs of notepads, 2 packs of erasers, and 10 packs of markers.

30/5=6
30/15=2
30/3=10

2. What is the x-intercept for the equation -2x + 5y = -10?

Answers

Answer:

Step-by-step explanation:

X intercept occurs when y = 0

-2x + 5(0) = -10

x = -10/-2

x = 5

Which mixed number is equivalent to the improper fraction 4 2/5?

4 2/5

7 4/5

8 2/5

9 3/5

Answers

the answer is 4 2/5, and I don't think others are equivalent to it

Dose any one know the answers for geometry A: A semester exam
PLZ I NEED HELP FAST!!

Answers

Answer:

Step-by-step explanation:

82 +9=5000 thank me later

The following graph shows a proportional relationship.
What is the constant of proportionality between yyy and xxx in the graph?

Answers

Answer:

The constant of proportionality is thus 1

Step-by-step explanation:

Note that the green line passes through (6, 6) and has a y-intercept of 0.  Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.

The constant of proportionality is thus 1, which is also the slope of this line.

A certain stock sold for $56.12 on Monday. On Tuesday it sold for $60.19. Find the increase in the price of the stock from Monday to Tuesday

Answers

Answer:

$ 4.07

Step-by-step explanation:

The problem is asking for the Increase in the stock price from Monday to Tuesday, meaning they want to know the difference between the stock price on Monday and Tuesday.

So we subtract Monday's price from Tuesday's price.

$60.19- 56.12 = $4.07

Why does demand for a product or service play a significant role in starting a new business?

Answers

Answer:

Basic economics like demand should important to you whether you run a seasonal business, buy a vacation property for passive income, or run a more traditional firm.

Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the
cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, c, Noah can use on each sandwich
How many ounces of cheese can Noah use on each sandwich?

Answers

Answer:

4 ounces

Step-by-step explanation:

6c = 24

c = 4

Answer: Noah can use 4 ounces per sandwich

an equation is c=24/6

Step-by-step explanation:

What is m<6
A.80
B. 100
C.70
D.110

Answers

Step-by-step explanation:

to fully answer we would need to see at least one specific size (segment lengths, angle sizes).

but there is not one in the whole visible picture. so, everything just stays relative.

just be the presentation in the picture, angle 6 is larger than 90 degrees. so, B or D would be right.

if it helps you, it is clear that 6 = 1 = 9 = 14 = 180-2 = 180-5 = 180-10 = 180-13.

the original price of a jacket was $74.00 .A store manager marked the price down by
25 1/2% . By how much was the price reduced?

Answers

If you mean reduced by 25.5%, then it got reduced by 34.46

74 = 100%
1.35 = 1% --> 100% : 74 = 1.35
34.46 = 25.5%

the new price is 39.54

PLEASE HELP FAST!!!
3
11
2
Which ordered pair is a solution to the system of linear equations 3 x- y- fo and x+By-to-
10?
O
12
o 5.3
21
o 35
21
3:5

Answers

Using the elimination method, multiply the first equation by 60 and the second one by 30 (least common denominators)

30x-45y=11...(1)
12x+5y=9...(12)

Multiply the second equation by 9, to eliminate y

30x-45y=11
+ 108x+45y=81
———————-
138x=92
x=92/138 (reduce fraction with 46)
x=2/3

Substitute x=2/3 into equation 2
12(2/3x)+5y=9
y=1/5

Therefore, the solution to the system is C. (2/3, 1,5)

read what on the image then answer

Answers

Fraction 10/12 would be greater than 3/4

Will mark brainly!

What is the inverse of [tex]f(x)=\frac{2}{x-1} +6?[/tex]
[tex]f^{-1} (x)=\frac{2}{x-1} +6[/tex]
[tex]f^{-1} (x)=\frac{2}{x} +7[/tex]
[tex]f^{-1} (x)=\frac{2}{y-6} +1[/tex]
[tex]f^{-1} (x)=\frac{2}{x-6} +1[/tex]

Answers

Answer:

[tex] {f}^{ - 1} (x) = \frac{2}{x - 6} + 1[/tex]

Step-by-step explanation:

we will subistitute f(x) by y and solve the equation in order to get the value of x,

then we subistitute x by y and y by x and y=f^-1(x)

A line L is parallel to the line 2x-5y-8=0. What is the gradient of the line

Answers

Answer:

2/5

Step-by-step explanation:

1) rearrange the equation in the form y=mx+c where m is the gradient and y is the y intercept

2x-5y-8=0

add 5y to both sides

2x-8=5y

divide 5 on both sides

2/5x - 8/5 = y

overall equation is y=2/5x-8/5

the gradient is 2/5

On a certain hot​ summer's day, 421 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $788.50. How many children and how many adults swam at the public pool that​ day?

There were _ children at the public pool.

There were _ adult at the public pool

Answers

Answer:

214 children and 207 adults

Step-by-step explanation:

214 x 1.75=374.5

207 x 2 = 414

414 + 374.5 = 788.5

Can somebody help me :

Answers

Answer:

A

Step-by-step explanation:

Negative numbers are smaller than positive numbers.

Answer:

Your correct 6.55 is a positive number while -6.5 is negitive and positive numbers are always larger then negitive ones

Hope This Helps!!!

Write the quadratic equation whose roots are 1 and -2, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
I = 0
х
5
?
Save For Later
Su
Check
2021 Mc LLC All Rights Reserved tesof Use Peso
O

Answers

Answer:

See below

Step-by-step explanation:

The quadratic equation in factored form:

a(x - α)(x - β), where a- leading coefficient, α and β - roots

We have:

a = 3, α = 1, β = -2

Substitute them to get:

3(x - 1)(x + 2)

Converting this into standard form:

3(x - 1)(x + 2) =3(x² + x - 2) =3x² + 3x - 6

NEED HELP NOW!!!
Properties of Perpendicular Bisectors Properties of Both Perpendicular Bisectors and Angle Bisectors Properties of Angle Bisectors
The bisector passes through the midpoint of a segment

The bisector is equidistant from the endpoints of the segment

The bisector can only exist if the original figure is a line segment.

The bisector cuts the original figure into two congruent parts.

The bisector is equidistant from portions of the figure.

Only one of each type of bisector exists in a plane.

The bisector passes through the interior of an angle.

The bisector creates a right angle with the figure.

The bisector is equidistant from the sides of the angle.

Which piece of information is incorrectly placed in the table?

A. The bisector cuts the figure into two congruent parts.
B. The bisector is equidistant from portions of the figure.
C. The bisector passes through the midpoint of a segment.
D. The bisector creates a right angle with the figure.

Answers

D.

Explanation:

a landscape of farmland bisected by long straight roads"

divide into two parts.

hope I help you ☺️❤️

:) :>

How many Match sticks will be In Image 6?​

Answers

19

In the first image, we are given 4 match sticks.

In the second image, we are given 7 match sticks. The difference between the match sticks is 3.

In the third image, we are given 10 match sticks. The difference between the match sticks again is 3.

If in the third image we are given 10 match sticks, and for every new image, there is another 3 match stick added, then in the sixth image, there must be 19 match sticks. Image 4: 10 + 3 = 13. Image 5: 13 + 3 = 16. Image 6: 16 + 3 = 19.

Answer = 19. Hope this helps. :)

Answer:

19

Step-by-step explanation:

Other Questions
__H2 + __SO2 > __H2S + __H2O identify the proper coefficients Versailles treaty Please help (30points) what regular polygon has an interior angle of 156 degrees Read the excerpt then choose the correct way to complete the sentence. What must a presentation contain to be called a multimedia presentation? Answers: two different types of media delivering two different messagesone form of media delivering several different messagestwo different forms of media focused on the same messagea single form of media focused on multiple messages The product of two irrational numbers is______ rational Please tell me if I am right with 1. And 3. Also, please help me with 2. And 4. Thanks! The area of rhombus is 360cmsquare and one of its diagonalis 18cm. Find the other diagonal. who else is transgendered? A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 1800 cubic feet.Find the dimensions of the pool. What volume in liters of carbon dioxide will be produced by the reaction of 18.5 liters of oxygen gas at STP? L CO2C3H8(g) + 5 O2(g) --> 3 CO2(g) + 4 H2O(g)**Report your answer to the correct number of significant digits! how did the slik road help the people of central asia The underlined section is referred to as a(n) couplet. You are a little bit nervous because you dont like speaking in public. You would rather just listen, but your teacher has explained that everyone in the group should contribute to the discussion. Choose the best way to be a good participant. -Come in strong. Be assertive and aggressive so that you speak before anyone else. -Decide on your own agenda for the discussion. You will know exactly what to say. -Decide what about the topic is meaningful to you. Take notes and find a good time to speak up. -Listen to all the participants speaking. Add a comment only if you have the same ideas. One of the impacts of the spread of Umayyad andAbbasid dynasties is that there was a lot more interactionwith a variety of people. There was a lot of tradehappening; of materials, language and religion. They wouldhave traded with the Byzantine empire for silks. The traderoute for this was called the Which graph represents the function? Please answer these!!!! :D Which answer choice is it show proof If the sales tax in your town was 7%, and you paid $1,400 in sales tax on your new car, then what was the originalprice of the car? And what is the total price including sales tax?Please be accurate of your answer and explain. 9490 divided by 5.explain how you got the answer