What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 6x3 − 3x2 + 5x + 9?

Answers

Answer 1

Answer:

Positive Roots: 2 or 0

Negative Roots: 1

Step-by-step explanation:

  f (x) = 6x3 − 3x2 + 5x + 9

To find the possible number of positive roots, look at the signs on the coefficients and count the number of times the signs on the coefficients change from positive to negative or negative to positive.

  f (x) = 6x3 − 3x2 + 5x + 9

Since there are 2 sign changes from the highest order term to the lowest, there are at most 2 positive roots (Descartes' Rule of Signs). The other possible numbers of positive roots are found by subtracting off pairs of roots (2 − 2).

Positive Roots: 2 or 0

To find the possible number of negative r oots, replace x with −x and repeat the sign comparison.

  f (−x) = 6(−x)3 − 3(−x)2 + 5 (−x) + 9

Simplify each term.

  Apply the product rule to −x.

     f (−x) = 6 ((−1)3x^3) − 3(−x)^2 + 5 (−x) + 9

   Raise −1 to the power of 3.

     f (−x) = 6 (−x^3) − 3(−x)^2 + 5 (−x) + 9

   Multiply −1 by 6.

     f (−x) = −6x^3 − 3(−x)^2 + 5 (−x) + 9

   Apply the product rule to −x.

     f (−x) = −6x^3 − 3 ((−1)^2(x^2)) + 5 (−x) + 9

Raise −1 to the power of 2.

     f (−x) = −6x^3 − 3 (1x^2) + 5 (−x) + 9

Since there is 1 sign change from the highest order t erm to the lowest, there is at most 1 negative

root (Descartes' Rule of Signs). Negative Roots: 1

The possible number of positive roots is 2 or 0, and the possible number of negative roots is 1. Positive Roots: 2 or 0

Negative Roots: 1


Related Questions

Help Pleaseeeeeeeeeeeeee!!!!!!!!! Help!!!!!!!

Answers

Answer:

i think its C and E

Step-by-step explanation:

( correct me if im wrong, i hope this helps!! )

I believe its C and E :))

Anna is selling boxes of cookies and tubs of popcorn for a Student Council fundraiser. On Monday, she made $40 selling 4 boxes of cookies and 2 tubs of popcorn. On Tuesday, she made $35 selling 1 box of cookies and 3 tubs of popcorn.

Write a system of equations to represent the cost of a box of cookies, x, and the cost of a tub of popcorn, y.

Answers

Answer:

5 boxes of cookies and 5 tubs of popcorn = $75

Step-by-step explanation:

To find y divide what is sold by 4 boxes of cookies and x by 2 tubs of popcorn.

The solution is

The cost of box of cookies x = $ 5

The cost of tub of popcorn y = $ 10

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the cost of cookies be = x

Let the cost of popcorn be = y

And ,

On Monday, Anna made $40 selling 4 boxes of cookies and 2 tubs of popcorn

Substituting the values in the equation , we get

4x + 2y = 40   be equation (1)

And ,

On Tuesday, Anna made $35 selling 1 box of cookies and 3 tubs of popcorn

Substituting the values in the equation , we get

x + 3y = 35   be equation (2)

On simplifying both equations , we get

Multiply equation (2) by 4 , we get

4x + 12y = 140   be equation (3)

Subtracting equation (1) from equation (3) , we get

10y = 140 - 40

10y = 100

Divide by 10 on both sides of the equation , we get

y = $ 10

So , the cost of tub of popcorn is $ 10

Substituting the value of y in equation (2) , we get

x + 3y =  35

x + 30 = 35

Subtracting 30 on both sides of the equation , we get

x = $ 5

So , the cost of box of cookies is $ 5

Hence , the cost of cookies is $ 5 and cost of popcorn is $ 10

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

It is known that the distance in metres through which a body falls freely varies directly as the square of the time taken. If a body falls through 80 metres in 4 seconds, find the distance it would fall in 5 seconds.

step-by-step easy explanation, please.

Answers

Answer:

K = 5 ; 125 m

Step-by-step explanation:

body falls through 80 metres in 4 seconds, find the distance it would fall in 5 seconds.

Given that:

Distance α (Timetaken)²

Distance = d ; Timetaken = t

d = Kt²

K = constant of proportionality

80 = k4²

80 = 16k

K = 80 / 16

K = 5

Distance it would fall in 5 seconds ; t = 5

D = Kt²

D = 5 * 5²

D = 5 * 25

D = 125

It will fall a distance of 125 m in 5 seconds.

Find the measure of each angle. a. Angle A = ? b. Angle B = ? c. Angle C = ?

Answers

Answer:

angle A=140

angle B=105

angle C=60

angle A=140

angle B=105

angle C=60

Step-by-step explanation:

PENN

What is an angle that is supplementary KFA?


Answers

Given:

A diagram.

To find:

An angle that is supplementary to ∠KFA.

Solution:

Supplementary angle: Two angles are called supplementary angles if they are lie on the same side of a straight line and their sum is 180 degrees.

From the given diagram, it is clear that ∠KFA lies on the intersection of lines HL and IK.

∠KFA and ∠DFA lie on the same side of a straight line IK.

∠KFA and ∠KFL lie on the same side of a straight line HL.

So, ∠DFA and ∠KFL are the angles supplementary to ∠KFA.

We need only one supplementary angle. So, we write either ∠DFA or ∠KFL.

Therefore, an angle that is supplementary to ∠KFA is ∠KFL.

4km : 370m in simplest form

Answers

Answer:

2km to 185 meters

Step-by-step explanation:

Identify the slope and y- intercept y=2x + 2

Answers

Answer:

Slope:2

Y-int:2

Step-by-step explanation:

y=m(slope)x+b(y-int)

Answer:

Slope is 2, Y-intercept is 2

Step-by-step explanation:

Point-slope form is y=mx+b

m=slope

b=y-intercept

Hope this helped.

The online store charges a flat rate of $4.99 for shipping. Ashley is buying a book for $21.93. She could buy the same book with a hardcover for $2.50 more.

Answers

Can u please type the full question

What is the value of (4)5/(4)3?

Answers

(4*5)/(4*3)
= 20/12
= (Now, we will simplify this equation and the least common multiple of 20 and 12 is 4 so, we will divide both 20 by 4 and 12 by 4 to get our answer in simplest and lowest form.
= (20 divided by 4)/(12 divided by 4)
= 5/3

So, in conclusion, the value of this question is 5/3.

Find the missing side or angle.
Round to the nearest tenth.
b=26
a=25
c=5
B=[? ]°

Answers

~96°






mmmmmmmmmmmmmmmmmmm

Answer:

The anwer for Acellus people is B=96 degrees

Step-by-step explanation:

Do this worksheets if someone do I will make him or her brainly if correct.

Answers

Answer:

in the picture above

Step-by-step explanation:

I hope that it's a clear solution and explanation.

The dimensions of a cylindrical water tank are shown below.
18 yd
o
58,320 yd
3,240 yd
60 yd
O
19,440 yd
15,270 yd3

Which of the following is the best estimate of the volume of
this water tank?

Answers

umm honestly it would be 58,320 yd

He me out with this question

Answers

Answer:

I believe the answer is B.

Help plssss with my exit ticket

Answers

Answer: 200.96 ft^2

Step-by-step explanation:

area of circle = (3.14 (pi))r^2

Radius is 6 (16 (the diameter)/2 = 8)

Answer:

Answer is H 200.96 :) Have a Happy Thursday!!

answered
A swimming pool containing 2000l of water is 1/16 full. How many litres of water is required to make the pool half full

1
SEE ANSWER

Answers

Answer:

16,000 liters

Step-by-step explanation:

Assuming the pool does not curve in any direction and is a big box with 90° corners:

1/16. 2,000 liters

2/16. 4,000 liters

3/16. 6,000 liters

4/16. 8,000 liters

5/16. 10,000 liters

6/16. 12,000 liters

7/16. 14,000 liters

8/16. 16,000 liters

9/16. 18,000 liters

10/16. 20,000 liters

Answer:

Half full = 16,000 liters

Need to add 14,000 more liters

Step-by-step explanation:

Proportions and Fractions

The swimming pool contains 2,000 liters of water and it's said to be 1/16 full. this means that the total capacity of the pool is:

2,000 liters * 16 = 32,000 liters

It's required to calculate how many liters of water are required to make the pool half full.

This can be found by dividing the above number by 2, thus:

Half capacity of the pool = 32,000 / 2 = 16,000 liters

We'll provide the following answer in case it's required.

To reach half capacity, it would be necessary to add

16,000 liters - 2,000 liters = 14,000 liters of water to the existing amount.

The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $633 and standard deviation σ = $45.
(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)
(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.09? (Round your answer to the nearest dollar.)
$

Answers

Answer:

(a) 0.3863

(b) $693

Step-by-step explanation:

Mean μ = $633

Standard deviation σ = $45.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)

We solve this question using the z score formula

z = (x-μ)/σ

where:

x is the raw score

μ is the population mean

σ is the population standard deviation.

For x > $646

z = $646 - $633/$45

z = 0.28889

Probability value from Z-Table:

P(x<646) = 0.61367

P(x>646) = 1 - P(x<646) = 0.38633

Approximately = 0.3863

The probability that the actual costs will exceed the budgeted amount is 0.3863

(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.09? (Round your answer to the nearest dollar.

Let the budgeted amount = x

Converting 0.09 to percentage = 0.09× 100% = 9%

100 - 9% = 91%

We find the z score of 91%

= 1.341

We are to find x

Using z score formula

z = (x-μ)/σ

1.341 = x - 633/45

Cross Multiply

1.341 × 45 = x - 633

60.345 = x - 633

x = 60.345 + 633

x = $693.345

Approximately to the nearest dollar is $693

a line is parallel to y=-2x+1 and intersects the point (4,1). what is the equation of this parallel line

Answers

Answer:

y=-2x+9

Step-by-step explanation:

A soccer team is saving money to buy new uniforms. The total cost for the uniforms is $88.74. There are 9 players on the team, and each player needs to save the same amount.

How much money does each player need to save?

A
$9.86

B
$98.60

C
$798.66

D
$788.66

Answers

Answer: A

Step-by-step explanation: $88.74÷9=$9.86

$88.74 is the total amount

9 players, and each player has to pay the same amount

we have to divide it evenly in 9 pieces, so we divide $88.74 into 9 groups which then equals $9.86

Hope this helps!

Need answer ASAP. Will give brainliest

Answers

Answer:

b

Step-by-step explanation:

V 34

Answer:

B

Step-by-step explanation:

credit to the other person

✓15
Is this rational or irrational

Answers

Answer:

irrational

Step-by-step explanation:

√15 is not a rational number it's a irrational number

:-))

Answer:

Irrational

Step-by-step explanation:

Rational numbers are those that can be written in the form a/b where a and b are both integers with no common factors.

sqrt15 cannot be written in that form, therefore it is irrational.

36 over 9 = g over 1​

Answers

Answer:

4/1

Step-by-step explanation:

g is 4

I need help finding JKLM

Answers

Answer:

JKLM = 96 in^2

Step-by-step explanation:

294/21 = 14

21/12 = 14/x

21 * x = 12 * 14

21x=168

x=8

A = L*W

A=12*8

A=96 in^2

Solve.
y= 2x + 4
y= 2x2

Answers

Answer:

5 terms

Step-by-step explanation:

Find the slope of the line going through the given pair of points.
(-4, 0) and (0, -3)

Answers

Answer:

Step-by-step explanation:

Slope = (difference of y-coordinates)/(difference of x-coordinates) = (0-(-3))/(-4-0) = 3/(-4) -3/4

Pls help extra points and mark brainlist easy reading

Answers

Answer:

sneaking

Step-by-step explanation:

please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!

(lol optional): add my sc: tealyn337

EFGH is an isosceles trapezoid. If EH=4x-27 and FG=x+9, find the value of x.
PLEASE HELP ASAP!

Answers

Answer:

If EFGH is an isosceles trapezoid,

if

EH=4x-27+

FG=x%2B9+

EG=3y%2B19

FH=11y-21

then EH=FG and EG=FH

set up equations:

4x-27=x%2B9 .......solve for x

4x-x=27%2B9

3x=36

x=36%2F3

3y%2B19=11y-21.......solve for y

11%2B19=11y-3y

30=8y

y=30%2F8

y=15%2F4

y=3.75

so,x=12    and y=3.75

you can also check the length of equal sides and equal diagonals:

EH=4%2A12-27+=21

FG=12%2B9+=21

EG=3%283.75%29%2B19=30.25

FH=11%283.75%29-21=30.25x=12

Step-by-step explanation:

y - 6 + x; use x = 6, and y = -2

Answers

Answer:

If you want y-6+x solved, it's -2

Step-by-step explanation:

Substitute 6 for x and -2 for y and you get (-2 - 6 + 6 =?). -2 - 6 = -8. -8 +6 = -2.

Simple way to do this is the given -6 and the 6 cancel out and that leaves the -2 from the y.

what is the reciprocal of -1/5

Answers

Answer:

5/-1

Step-by-step explanation:

The reciprocal is just flipping the fraction.

What is equivalent to 5^3•5^4

Answers

Answer:

[tex] {5}^{7} [/tex]

Step-by-step explanation:

[tex]5^3•5^4 = {5}^{3 + 4} = \purple{ \bold{ {5}^{7} }}[/tex]

need help SHOW YOU WORK PLS

Answers

Starry Sky charges $34.50 an hour, Solar R' Us charges $28.60 and Lights On Us charges $26.17. The best option is Lights On Us. To get the answer just divide the total price by the number of hours.
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