Question

Totally Confused regarding Rational Root Theorem + Descartes Rule of Signs!

Answer 1

What are the possible rational zeros of f(x) = 2x3 − 15x2 + 9x + 22?

Answer 2

± 1, ± 2
± 1, ± 2, ± 11, ± 22
± 1, ± 1 over 2, ± 2, ± 11 over 2, ± 11, ± 22
± 1, ± 1 over 2, ± 1 over 11, ± 1 over 22, ± 2, ± 2 over 11

Answer 3

@Directrix

Answer 4

@phi

Answer 5

Can you help me?

Answer 6

@ikram002p

Answer 7

@KendrickLamar2014

Answer 8

@Loser66 @johnweldon1993 @uri @jhonyy9

Answer 9

https://www.youtube.com/watch?v=Qr9aqzdLx4k

Answer 10

:I

Answer 11

I was expecting you to help me out via communication

Answer 12

wait what

Answer 13

I'm lost

Answer 14

I know about coefficients

Answer 15

But i'm wondering how you would apply this to all problems.

Answer 16

Like I said, I dont want answers :P

Answer 17

I wanna learn

Answer 18

https://answers.yahoo.com/question/index?qid=20101214192907AAfqVem

Answer 19

^^^

Answer 20

Can you chime in Xavier?

Answer 21

?

Answer 22

I just still dont understand

Answer 23

Look at the youtube link than

Answer 24

w/e

Answer 25

thanks for posting links atleast

Answer 26

_-_

Answer 27

https://www.youtube.com/watch?v=aNtxUkbVE-4

Answer 28

https://www.youtube.com/watch?v=8jvv4zGD0_M

Answer 29

Can you factor the polynomial?

Answer 30

Yes.... i think

Answer 31

How does factoring have to do with this?

Answer 32

Oml

Answer 33

Please help me out :(.

Answer 34

Try factoring 2x^3 -15x^2 +9x

Answer 35

What do you mean by factoring... like synthetic division?

Answer 36

Factoring (called "Factorising" in the UK) is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

Answer 37

What i'm wondering is how to solve the problem, I don't know how factoring has to do with it though.

Answer 38

You know x is a factor, how else can you break it apart bit by bit?

Answer 39

2x^2 * 2x^1?

Answer 40

?

Answer 41

After you factor the problem, that is find each component, the zeroes will be easy to see.
You want to represent it so that every term is fully factored

Answer 42

Can't I just use the coefficient of the first and last term? Find the factors of both of them (22=1,2,11,22) and do them on top of the first term (2=1,2)?

Answer 43

Atleast that's what i'm thinking?

Answer 44

No, look x( x ( 2x-15) + 9 ) +22 is something you can get if you just think about the components of the function

Answer 45

So what would you use that for?

Answer 46

Use it to break it down further...

The idea is to get something resembling a(x+b) + c(x+d) + C so when x=-d that is root of the function or an x value where the whole function become zero

Answer 47

b = d in this case

Answer 48

So factors of 22/factors of 2?

Answer 49

22 is just a constant outside nothing to do our variable

Answer 50

Wait, I think I knda get it now without doing what you are asking... please let me know whether its right or not.

Factors of 2: 1,2

Factors of 22: 1,2,11,22

Factors of 22/2

1/1 = 1, 1/2, 2/1=2, 2/2=1 (we have that), 11/1=11,11/2, 22/1 22/1=11(we already have that.

So the answer would be C?

Answer 51

@daniel.ohearn1

Answer 52

@uri

Answer 53

no-one?

Answer 54

:(

Answer 55

Looking at P(-x)

Answer 56

How many times does the polynomial change signs?

Answer 57

2

Answer 58

looks like one to me

Answer 59

2(-x)^3 is negative
-15(-x)^2 is negative
9(-x) is negative
and 22 is positive

Answer 60

HI!!

Answer 61

What are the possible rational zeros of \( f(x) = 2x^3 − 15x^2 + 9x + 22\)

Answer 62

3

Answer 63

take all fractions where the numerator goes in to 22 evenly (so 1,2,11,22) and the denominator goes in to 2 evenly (so 1 and 2)
don't forget the \(\pm\) since they could be positive or negative

Answer 64

the list is fairly long, but not too long
if you divide by 1 you get the whole number, so a start is \[\pm1,\pm2,\pm11,\pm22\]

Answer 65

then divide all those by 2 and you are done

Answer 66

Desc Rule of Signs says that if there are only 2 sign changes there can only be one or two negative roots right??

Answer 67

so factors of 22/factors of 2

Answer 68

this questions seems to only ask for the rational root theorem
descartes rule of sign tells you something else, namely how many possible positive and negative roots there are

Answer 69

okay, can you help on a problem that talks about descartes?

Answer 70

sure why not?

Answer 71

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

Positive Real: 1
Negative Real: 0
Complex: 2
Positive Real: 1
Negative Real: 2 or 0
Complex: 2 or 0
Positive Real: 2 or 0
Negative Real: 1
Complex: 2 or 0
Positive Real: 2 or 0
Negative Real: 2 or 0
Complex: 1

Answer 72

Yes, but acknowledging only descartes narrows it down big time

Answer 73

Looking at your poss. answers

Answer 74

what really narrows it down is finding them
all this muck is an artifact of history, not something useful today

Answer 75

not true, if you want to build something with this sort of shape

Answer 76

or if you want to travel across it

Answer 77

can i get help on the problem either way :)?

Answer 78

\[f(x) = 6x^3 − 3x^2 + 5x + 9\] the coefficients have two changes in sign
from \(+6\) to \(-3\) and fron \(-3\) to \(+5\)
that means there are either 2 or no positive zeros (you count down by twos)

Answer 79

I think its the 3rd one

Answer 80

now you have to consider \(f(-x)\) which in this case is \[f(-x)=-6x^2-3x^2-5x+9\]
how many changes in sign here?

Answer 81

1?

Answer 82

right
so there must be a negative root
since you count down by twos, and you cant have minus one negative roots !

Answer 83

so 1 negative root?

Answer 84

definitely one

Answer 85

no more, no less

Answer 86

Then the complex would be 2

Answer 87

could be 2 or could be none, depending on whether there are 2 or no positive ones
both are possible, 2 positive, no complex or 2 complex, no positive

Answer 88

ok