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

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:

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 ☺️❤️

:) :>

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:

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

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

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

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.

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

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:

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

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)

read what on the image then answer

Answers

Fraction 10/12 would be greater than 3/4

can someone plz help me I need the answer asap ​

Answers

Answer:

no. c is the correct answer

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

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

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)

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.

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

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

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!!

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!!!

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

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

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

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.

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

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

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.

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:

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
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