If (x+5) is one of the factors of the polynomial x3 + x2 - 32x - 60, find the remaining roots.

Answers

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

x = 5

x = 2

x = -6

Step-by-step explanation:

Use synthetic division to determine whether x – 4 is a factor of:

–2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

For x – 4 to be a factor, you must have x = 4 as a zero. Using this information, I'll do the synthetic division with x = 4 as the test zero on the left:

completed division

Since the remainder is zero, then x = 4 is indeed a zero of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4, so:

Yes, x – 4 is a factor of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

Find all the factors of 15x4 + x3 – 52x2 + 20x + 16 by using synthetic division.

Remember that, if x = a is a zero, then x – a is a factor. So use the Rational Roots Test (and maybe a quick graph) to find a good value to test for a zero (x-intercept). I'll try x = 1:

completed division

This division gives a zero remainder, so x = 1 must be a zero, which means that  x – 1 is a factor. Since I divided a linear factor (namely, x – 1) out of the original polynomial, then my result has to be a cubic: 15x3 + 16x2 – 36x – 16. So I need to find another zero before I can apply the Quadratic Formula. I'll try x = –2:

completed division

Since I got a zero remainder, then x = –2 is a zero, so x + 2 is a factor. Plus, I'm now down to a quadratic, 15x2 – 14x – 8, which happens to factor as:

(3x – 4)(5x + 2)

Then the fully-factored form of the original polynomial is:

15x4 + x3 – 52x2 + 20x + 16

= (x – 1)(x + 2)(3x – 4)(5x + 2)

Given that  x = -3 + sqrt(11)   is a zero of x4 + 6x3 – 7x2 – 30x + 10, fully solve the

equation x4 + 6x3 – 7x2 – 30x + 10 = 0.

Since they have given me one of the zeroes, I'll use synthetic division to divide it out:

completed division

(You will probably want to use scratch paper for the computations required when manipulating the radical root.) Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Since you only get these square-root answers by using the Quadratic Formula, and since the square-root part of the Formula is preceded by a "plus-minus" sign, then these square-root answers must always come in pairs. Thus, if x = -3 + sqrt(11) is a root, then so also must x = -3 - sqrt(11) be a root. So my next step is to divide by x = -3 - sqrt(11):

completed division

I had started with a fourth-power polynomial. After the first division, I was left with a cubic (with very nasty coefficients!). After the second division, I'm now down to a quadratic (x2 + 0x – 5, or just x2 – 5), which I know how to solve:

x = +/- sqrt(5)

Then the full solution is:

x = -3 +/- sqrt(11), +/- sqrt(5)

If you have studied complex numbers, then you may see a problem of the following type.

Given that 2 – i is a zero of x5 – 6x4 + 11x3 – x2 – 14x + 5, fully solve the

equation  x5 – 6x4 + 11x3 – x2 – 14x + 5 = 0.

They have given us a zero, so I'll use synthetic division and divide out 2 – i:

completed division

(You will probably want to use scratch paper for the computations required when doing complex division.)

Recall that, to arrive at a zero of 2 – i, they must have used the Quadratic Formula, which always spits out complex answers in pairs. That is, you get the imaginary part (the part with the "i") from having a negative inside the "plus or minus square-root of" part of the Formula. This means that, since 2 – i is a zero, then 2 + i must also be a zero.  So I'll divide by 2 + i:

completed division

This leaves me with a cubic, so I'll need to find another zero on my own. (That is, I can't apply the Quadratic Formula yet.) I can use the Rational Roots Test to help find potential zeroes, and a quick graph of x3 – 2x2 – 2x + 1 can help. I will try x = –1:

completed division

Now I'm down to a quadratic (x2 – 3x + 1, which happens not to factor), so I'll apply the Quadratic Formula to get:

x = (3 +/- sqrt(5))/2

Then all the zeroes of x5 – 6x4 + 11x3 – x2 – 14x + 5 are given by:

x = 2 - i, 2 + i, (3 - sqrt(5))/2, (3 + sqrt(5))/2, -1


Related Questions

Determine the intercepts of the line.
y = 80 - 18

Answers

Answer:

Step-by-step explanation:

This equation is in slop-intercept form. This means that the y-int is in the equation, it will always be the constant, so y is -18.

To find x, set y to 0.

0 = 8x - 18

18 = 8x

18/8 = x

9/4 = x

Solve the problem. Show your work

Answers

Answer:

D correct

Step-by-step explanation:

WILL GIVE BRAINLIEST
On a field trip, there are 8 adults and 24 students. What is the ratio of students to the total number of people on the field trip?

8 to 24
3 to 4
1 to 4
32 to 24

Answers

Answer:

3:4

Step-by-step explanation:

24 students : 32 people total

Divide both sides by 8

Answer: 3 to 4

this is correct, verified it myself B)

a bowl contains 15 gra

Answers

Answer: hi

Step-by-step explanation:

Answer:

And, so...

What about the 15 grams?

Diyva has 70 rocks.she donates half of the rocks to a science center. then she collects 3 rocks on each of her nature hikes

Answers

Answer:

What are you asking here? This is more like a statement.

Step-by-step explanation:

Answer:

I'm just going to assume that your trying to figure out how many rocks she has left, in which case the answer would be 38.

I need help with this, Its geometry

Answers

Answer:

Step-by-step explanation:

x + 17 + 6x + 10 + 4x - 34 = 180

11x + 27 - 34 = 180

11x - 7 = 180

11x = 187

x = 17

x + 17 = 17 + 17 =34

6(17)+10 = 102 +  10 = 112

4(17) - 34 = 68 - 34 = 34

Answer is D

please i need this quick , it’s so confusing

Answers

i think its A : 25 B : 81 C: 49

Brenda wants to buy a phone case that costs $35. It is on sale for 20% off. What would be the sales price? What are we finding?

A) part
B) whole
C) percent

Answers

Answer:

A

Step-by-step explanation:

What is the value for angle 2?

I need help

Answers

Answer:

120

Step-by-step explanation:

all complementary angles should add up to 180 degrees

Answer:

the value of 2 is 60

Step-by-step explanation:

Aiman has 6 pizzas to share at a party. If each person will eat 3/8 of a pizza, how many people can share the pizzas?
A 48 people
B 16 people
C 2 people
D 6 people

Answers

Answer:

The amswer is B, 16 people.

Which set of numbers does NOT describe the side
lengths of a right triangle?
a. 3, 4, 5
b. 5, 12, 13
c. 6, 14, 17
d. 7, 24, 25
4

Answers

Answer:

The answer is C

Step-by-step explanation:

You have to do the Pythagorean Theorem.

A. you get 25=25

B. you get 169=169

C. you get 232=289

D. you get 625=625

On a scavenger hunt, you find 16 out of 25 objects. Write "16 out of 25" as a fraction, a decimal, and a percent.
Fraction:
Decimal:
Percent:
I need help ASAP

Answers

Answer:

Fraction: 16/25 Decimal: 6.25 Percent: 6%

Step-by-step explanation:

I am 99.99% sure this is right.. I hope it helps you.

The statements "16 out of 25" written in fractional, decimal, and percent form are 16/25, 0.64, and 64% respectively.

What is a fraction?

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The Given statement is "16 out of 25".

The statement in mathematical form is:

16/25 (Fraction)

= 0.64 (Decimal)

= 64% (percent)

Hence, the statements "16 out of 25" written in fractional, decimal, and percent form are 16/25, 0.64, and 64% respectively.

Learn more on fractions here:

brainly.com/question/10354322

#SPJ2

best estimate for 7/8-6/11

Answers

Ummm we are allll gonna be dead cause Biden be da president

Answer:

WE ARE GONNA DIE

Step-by-step explanation:

BECAUSE BIDEN IS THE PRESIDENT AND DONALD TRUMP IS NOT. >.< I DONT LIKE BIDEN!!!!

WILL GIVE BRAINLIEST EASY

drag and drop correct answers

Answers

Answer:

X- int: -3,0 and 1,0

Y- int: -3, 0

Domain: -inf to +inf

Range:+in to -4

Minimum Value : -4, 1

Need help with geometry question

Answers

Answer:

B. 66

Step-by-step explanation:

idk how to explain it without repeating what it says in the answer

Answer:

The answer is:

B) 66 degrees

Step-by-step explanation:

Since the triangle is an isosceles triangle, angle C is the same as angle B.

57 + 57 = 114

Since you know two of the three angles, and you know that a triangle's angles must equal 180 degrees...

180 - 114 = 66

Angle A must equal 66 degrees for the triangle to equal 180 degrees.

I hoped this helped you! If it did, please consider rating and pressing the 'Thanks' button. Have great day!

Please answer correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

x=57 degree

Step-by-step explanation:

Answer:

x=57

Step-by-step explanation:

(x-5) + (2x+4) = 180

get all xs on the same side non xs on other side till you get

3x=171

then divide 171 by 3

x = 57

Wait So Do You Multiply Fractions Like Lets Say The Problem Was 2 x 9
8 1 Right So Do I Multiply 9x1 Then 1x2 Then 8x9 Then 8x2?
I Learned How To Do Them A While Ago But Forgot.

Answers

Answer:

can you take a photo of the question you're asking for? I can answer it, but your question was kinda worded funny so I don't rest understand what you mean. I'm good at fractions, so I will be happy to help:)

A rectangular garden has an area of 35 square miles. If its length is 78 miles, what is its width?
Input your answer as a fraction.

Answers

Answer:

9/20 mi

Step-by-step explanation:

A= b*hFill in the Values

35 = 78 * h

3. divide 35 by 78 = 0.44871794871

4. round that to .45

5. To make a fraction, put it over 100

45/100

7. Simplify fraction

9/20

Chin bought 12 pounds of apples for $6. Use the ratio table to find the cost of buying 3 pounds of apples. *

Answers

Answer: The answer should be 1.5.

Step-by-step explanation:

$6 divided by 12 is .5... Multiply .5 by 3, seeing as 1 pound = $.5

Answer:

$.5

Step-by-step explanation:

hope this helps y'all

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $24.6, and the standard deviation is known to be $7.9. How large of a sample would be required in order to estimate the mean per capita income at the 80% level of confidence with an error of at most $0.56? Round your answer up to the next integer.

Answers

Answer:

327

Step-by-step explanation:

Calculation for How large of a sample would be required in order to estimate the mean per capita income

First step is to find z 80% confidence level

At 80% confidence level the z will be:

α/2 = 1 - 80% = 1 - 0.80 = 0.20

α/2= 0.20 / 2 = 0.01

Zα/2= Z0.01= 1.28 from z table

Now let calculate the Sample size using this formula

Sample size = n= [( Zα/2* σ ) / E]^2

Let plug in the formula

n = (1.28*7.9/0.56)^2

n= 326.06

n=327 (Approximately)

Therefore How large of a sample would be required in order to estimate the mean per capita income will be 327

It also detects if you are right or wrong

Answers

Answer:

50

Step-by-step explanation:

all your doing is dividing 100 by 20 and u get 50

Answer: 15. A. Proportional 16. B. 50 mph

Step-by-step explanation: The price and the number of apples are proportional based on the info you have given us. And B. 50 is correct because 100 miles in 2 hours is 100/2 which equals 50/1 so the unit rate would be B. 50 mph.

PLEASE HELP ASAP
Factor 3x+6y-9z

Answers

I’m not sure what the answer is so better I don’t say I don’t want you to get it wrong

can someone help my sister with her module? she in 6th,and i am way to dumb to know how to help her (i gib link)

Answers

Answer:

Sure!

Step-by-step explanation:

What is the slope of this line?

Enter your answer as a fraction in simplest term in the box.

Answers

Answer:

1/4

Step-by-step explanation:

y2-y1/x2-x1

6-5/ 0 - -4.... since it's two subtract signs facing each other you turn it into a +..... 1 /4

Answer:

1/4

Step-by-step explanation:

y2-y1/x2-x1

6-5/ 0 - -4.... since it's two subtract signs facing each other you turn it into a +..... 1 /4

Need help!! How do I figure out the question.

Answers

Answer:

its the second one lol its just asking you to pick the one less than a and a is 0.11 so it would be 0.0019

Step-by-step explanation:

4 x 7/8 Pls I need help my mom is yelling at me

Answers

Answer:

3.5

Step-by-step explanation:

Answer:

7/2 or 3 1/2

Step-by-step explanation:

4 * 7/8 = 4/1 * 7/8 = 28/8 = 7/2 = 3 1/2

Dierections:Factor out the GCF from the following.Make sure your answer is factored completely by taking out any common numbers and or variables

Answers

Answer:

21

Step-by-step explanation:

your mom

what is the slope of the line passing through the points (0,-5) and (4,2)

Answers

Answer: 7/4.

Step-by-step explanation: To find the slope of a line, one must use the formula (y2-y1)/(x2-x1). In this case y2 is 2, y1 is -5, x2 is 4, and x1 is 0. We can plug this into the equation to get 7/4.

I don’t understand help me plz hard

Answers

Answer:

-2 1/2 is the correct answer

I hope this helps! If it is correct please mark brainliest answer, thank you!

Stay safe, God bless and happy studying!

Yesterday, the temperature in a city dropped from 9°C to –9°C, as shown below.



The expression 9 + (–18) represents the final temperature. Which of the following is an equivalent way to describe this temperature?

|–18| degrees in a negative direction from 9 degrees

|–18| degrees in a positive direction from 9 degrees

|–9| degrees in a negative direction from 9 degrees

|–9| degrees in a positive direction from 9 degrees

Answers

Answer:

I belive the correct answer might be (A)

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