Mathematics College

Find the zeros for each function
1. f(x)= x^3 + 12x^2 + 21x + 10

2. f(x) = x^4 + x^3 - 11x^2 - 9x + 18

Answers

Answer 1

9514 1404 393

Answer:

zeros are -10, and -1 (multiplicity 2)zeros are {-3, -2, 1, 3}

Step-by-step explanation:

For higher-degree polynomials I find it extremely useful to use a graphing calculator to find the zeros.

The usual approaches are ...

use the rational root theoremtry values of x=±1narrow the search using Descartes' rule of signsestimate maximum or minimum root values

__

1. Rational roots will be factors of 10, so ±1, ±2, ±5, or ±10. The signs are all positive, so there are no positive real roots. The sum of odd-degree coefficients is the same as the sum of even-degree coefficients, so -1 is one of the roots. Removing that using synthetic division gives you ...

   f(x) = (x +1)(x^2 +11 +10)

The quadratic (more or less obviously) factors as (x+1)(x+10), so the complete factorization is ...

  f(x) = (x +1)^2(x +10)

and the zeros are {-10, -1, -1}.

__

2. Rational roots will be factors of 18, so will be ±1, ±2, ±3, ±6, ±9, ±18. The sum of coefficients is 0, so x=1 is a root. The rule of signs tells you that there are 2 positive real roots, so there is one more positive real root. Synthetic division tells you the factoring so far is ...

  f(x) = (x -1)(x^3 +2x^2 -9x -18)

We note that the first two coefficients have the same ratio as the last two, so we can factor by grouping.

  x^3 +2x^2 -9x -18 = x^2(x +2) -9(x +2) = (x^2 -9)(x +2)

Factoring the difference of squares gives you the complete factorization, hence all of the roots. (The zeros are the values of x that make the factors zero.)

  f(x) = (x -1)(x +2)(x -3)(x +3)

The zeros are {-3, -2, 1, 3}.

Find The Zeros For Each Function1. F(x)= X^3 + 12x^2 + 21x + 102. F(x) = X^4 + X^3 - 11x^2 - 9x + 18
Find The Zeros For Each Function1. F(x)= X^3 + 12x^2 + 21x + 102. F(x) = X^4 + X^3 - 11x^2 - 9x + 18

Related Questions

39.4 x 1.7 I don’t how workout this out

Answers

Answer:the answer is 66.98

Step-by-step explanation:

An online camping supplies outlet charges $14 for a canteen,
and shipping is $2 per order.
Part A
Write an expression that CJ can use to find the total cost in
dollars for ordering n canteens.

Part B
CJ orders 2 canteens and his friend Cameron orders 4 canteens.
What is the total cost, including shipping, for both orders?
Show your work.

Answers

Answer:

Part A: 14x + 2

Part B: CJ's order is $30, and Cameron's order is $58.

Step-by-step explanation:

Part A: The total cost of the order would be $14 multiplied by the amount of canteens, plus the shipping price of $2. This is what my expression represents.

Part B:

CJ's Order:

14(2) + 2 =

28 + 2

$30

Cameron's Order:

14(4) + 2 =

56 + 2 =

$58

Hope this helps! :D

What is an equation of the line that passes through the point (-1,-7) and is perpendicular to the line x+y=6x

Answers

Answer: y = -1/5x - 36/5

Hope this is right with the weird fractions. Work in pic:

Juanita constructed a number line to test her brother’s understanding of opposites. She tested him on all points that were labeled with letters. Her brother had trouble representing the opposite of point A.

Which represents the opposite of Point A?
Negative (negative 10)
Negative (negative 5)
0
Negative (10)

Answers

Answer:

-(10)

Step-by-step explanation:

Answer:

negative (negative 10) is the answer.

Step-by-step explanation:

Identify the GCF of 36 and 24
6
12
2
8

Answers

Answer:

12...you already figured it out but alr

Step-by-step explanation:

Which algebraic expression is equivalent to the expression below?

--------------------------
(4n + 14) + (6 + 7n)
--------------------------

A. 24n + 7

B. 10n + 21

C. 18n + 13

D. 11n + 20

Answers

Answer:

D

Step-by-step explanation:

Combine like terms 4n can only be added with 7n and 14 can only be added to 6

Answer:

11n + 20

Step-by-step explanation:

Because all of the signs are + , the parentheses can be removed.

Next, combine like terms:

4n + 14 + 6 + 7n = 11n + 20

None of the three given possible answers is correct.

What is the slope of the line that passes through the points (-3, -9)(−3,−9) and (22, -4) ?(22,−4)? Write your answer in simplest form.

Answers

Answer:

1/5

Step-by-step explanation:

Equation: [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Points: (-3, -9) and (22, -4)

[tex]y_{2}[/tex] is the second y point that shows up on the question, basically go by order. So it's -4

[tex]y_{1}[/tex] is -9, because again, in order of which coordinates pop-up first in the question

[tex]x_{2}[/tex] is 22, [tex]x_{1}[/tex] is -3

Now input into the equation, to make it easier we'll split the fraction into 2 equations:

[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex] = [tex]y_{2} - y_{1}[/tex] and [tex]x_{2} - x_{1}[/tex], we'll put them back in a fraction later

[tex]y_{2} - y_{1}[/tex] = -4 - (-9) = -4 + 9 = 5

[tex]x_{2} - x_{1}[/tex] = 22 - (-3) = 22 + 3 = 25

now put it in the fraction, remember y on top x on the bottom:

5/25, simplify, 1/5

What is the domain of the relation shown?
will mark as branliest

Answers

Answer:

2 or 4

Step-by-step explanation:

Three people take 90 minutes to water a garden. How many minutes would six people take?

Answers

Answer:

45

Step-by-step explanation:

it will take 45 minutes for 6 people to water a garden

Answer:GIVEN

Three people take 90 minutes to water a garden.

TO DETERMINE

The time (minutes) taken by six people to complete the work

EVALUATION

SOLVE USING RULES OF THREE

Now if the Number of people increases then the time take taken will decreases

Here the number of people and Time taken are in inverse proportion

So the time required

FINAL ANSWER

The required time = 45 minutes

Step-by-step explanation:

How do you write this in a expression?please answer quick (take away a number n from 24)

Answers

Answer:

24-n

Step-by-step explanation: hope this helps if it does pls give brainliest tysm!

Answer:

24-n

Step-by-step explanation: we taking away so that is substraction.

Write an equation for the line that passes through (2,-1) and is parallel to the line y= 3x+8?

Answers

Answer:

y= 3x + 5

Step-by-step explanation:

If it is parallel it has the same slop so we know mx = 3x

then solve for b

-1 = 3(2) + b

-1 = 6 + b

5 = b

Please Help These Are All My Points.

Answers

im pretty sure it’s the second one i’m sorry if i’m wrong

plz help me on this final i beg of u!!!

Answers

Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

Its asking for how long did she watch for both videos.

[tex] \frac{3}{8} + \frac{1}{8} = \frac{4}{8} [/tex]

4/8 is half. so simplest form would be

[tex] \frac{1}{2} [/tex]

Answer:

1/2 minutes

Step-by-step explanation:

you add the two fractions together and because they have a common denominator you just add across.

1/8+3/8=4/8

now we simplify

the numerator and denominator can both be divided by 4.

4÷4=1

8÷4=2

1/2

What is the volume of a sphere with a diameter of 4 meters? (Use 3.14 for π.) 18.84 m 3 100.48 m 3 33.49 m 3 25.12 m 3

Answers

Answer:

Step-by-step explanation:

the formula for Volume of the sphere is

V=4/3 * π*r^3

diameter =4, r=2

V=4/3 * 3.14 * 8=33.49

There are49 students on a tour.Each guide can take 5 students.How many guides are needed?Explain.

Answers

10 because 9 is 45 and then there is 4 students left over who need a guide (please give brainliest:) )

Which pair shows equivalent expressions?

Help quick please!

Answers

Answer:

i think A

Step-by-step explanation:

Choose all that apply!!

Answers

Answer:

B and D. I think

It’s B and D........

100 points! hard problem!

Answers

Answer:never gonna give you up

Step-by-step explanation:by rick astley

"you wouldnt get this from any other guy and i just wanna ask you how your feeling, gotta make you underatnd, never gonna give you up, never gonna let you down."

nEvEr gOnnA giVe U uP

Will mark the brainliest

Answers

Answer:

C.

X = -5

Step-by-step explanation:

The age of a car and the value of the car
O Positive Correlation
O Negative correlation

Answers

ANSWER:

Positive Correlation

EXPLANATION:

The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.

Answers

Answer:62%    Step-by-step explanation:

what is the solution of sqaure root -4x = 100

Answers

Answer:

I’m pretty sure it’s -2500

Step-by-step explanation:

Answer:

I think it would be x = -2500

Step-by-step explanation:

You square both sides to get rid of the square root and get -4x = 10000 then divide 10000 by -4 to get -2500

Which statement(s) most directly apply to capitalism?

1. There is heavy government regulation of industry.
II. Individuals can start some, but not all, kinds of enterprises.
III. The price and availability of goods is determined primarily by the market.
a. I and II
b. ll only
c. I and III
d. Ill only

Answers

Answer:

The answer is D, lll only.

Step-by-step explanation:

Just took the test on e d g e!

The statement that most directly applies to capitalism is III only.

Option D is the correct answer.

What is capitalism?

It is a system of the economy where means of production and distribution are owned by the private, not the government.

We have,

The economic system of capitalism is characterized by private ownership of the means of production and distribution of goods and services, as well as the profit motive as the driving force behind economic activity.

Based on this definition, statement III most directly applies to capitalism, as it highlights the central role of market forces in determining prices and availability of goods.

On the other hand,

Statement I, which suggests heavy government regulation of the industry, is not a typical feature of capitalism, as it implies a more interventionist approach by the government in the economy.

Capitalism generally favors a more limited role for the government in economic affairs, although some government regulations may still be present.

Statement II, which suggests that individuals can start some, but not all, kinds of enterprises, is also not a defining characteristic of capitalism.

In a capitalist system, individuals are generally free to start any kind of enterprise that they wish, provided they can obtain the necessary resources and meet any legal or regulatory requirements.

Therefore,

The statement that most directly applies to capitalism is III only.

Learn more about  capitalism here:

https://brainly.com/question/28144254

#SPJ7

Tim predicts he will get 98 points on the next exam. If Tim actually earned 62 points, what was Tim's percent error?

Answers

Answer:

If Tim actually earned 62 points . Therefore Tim's percent error is 58.1 % .

Step-by-step explanation:

If I say I’m sick on Tuesday at 8pm and they say I have 72 hours till I can work again and I work at 12 am what time and what day will I work on?

Answers

Answer:

Saturday

Step-by-step explanation:

I think

There are 42 boys and 48 girls in sixth grade and each student must be assigned a home room. Each homeroom should have the same number of boys and the same number of girls.

what is thegreatest possible number of sixth grade students?

Answers

Answer:

50

Step-by-step explanation:

you add 42 and 48 i think

A .14kg baseball is dropped from rest. It has a momentum of .78kg x m/s just before it lands on the ground. For what amount of time was the ball in the air?

Answers

Answer

what r the options? a b c d?????

i wuld say it is 2.5

Step-by-step explanation:


If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?

Answers

Step-by-step explanation:

Given: Radius , r =21 cm

The angle at the center of the circle, n° =140°

Length of an arc =?

W.K.T Formula, Length of an arc = 2πr( n°÷360°) units

= 2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Answer:

2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Step-by-step explanation:

Kyoko is reading a book by her favorite author. She read the first 20 pages in One-half of an hour. Reading at the same pace, Kyoko wants to determine if she’ll have enough time to finish the book before she has to go to bed.

Answers

Answer:

It will take her 3 hours and 120 pages

Step-by-step explanation:

It was on edge pls mark brainliest

Answer:

b

Step-by-step explanation:

What is the best name of the line?

Answers

The radius is the answer
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