help !!!!

- anonymous

help !!!!

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- anonymous

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- Nnesha

use the p/q method
where \[\large\rm \frac{ p }{ q}= \frac{\pm ~~all~factors ~of~constant~term}{\pm~~all~factors ~of ~leading ~coefficient }\]

- anonymous

the leading coefficient is 8 and 10 right?

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## More answers

- Nnesha

there should be only one leading coefficient
coefficient of the highest degree variable

- anonymous

10?

- Nnesha

what's the highest degree (exponent ) ??

- anonymous

8 sorry

- Nnesha

yes correct write all factors of 8 and factors of constant term

- anonymous

3x^4+10x^3-11x^2-10x / 8?

- Nnesha

no. what's the constant term in that function ?

- anonymous

x?

- Nnesha

that's the variable
what would be the leading coefficient and constant term?
here is an example \[4x^2+3x+9\]
4 is leading coefficient(coefficient of highest degree variable )
cosntant term is 9( number without any variable )

- Nnesha

constant*

- anonymous

8 is the constant

- Nnesha

correct and leading coefficient is ?

- anonymous

11x^2

- Nnesha

what's the highest exponent in that function ?
if u look at my example it was 2 so that's how leading coefficient was 4
\[\large \rm Ax^5+Bx^3+C\]in this example highest exponent is 5 leading coefficient is `A`

- anonymous

3x^4

- Nnesha

that's the term
where just 3 is leading coefficient and
now what are the factors of 8 and 3 ?

- jim_thompson5910

@Nnesha is correct. Here is a slightly different way to look at it

##### 1 Attachment

- anonymous

you divide 8/3?

- anonymous

question (not to interrupt) does not ask for the "possible" rational zeros, it asks for the zeros

- Nnesha

no divide factors of 8 by the factors of of 3
i know they r looking for real zero so she can just graph it

- anonymous

it is not necessary to list all possible rational zeros of this, in fact it is mostly a waste of time
you want to find the actual zeros, not the possible rational ones, as there are many

- anonymous

unless you want to make a to see which ones to check

- anonymous

"make a list"

- jim_thompson5910

@satellite73 the idea is to generate all the possible rational roots
then you check each possible root in f(x). If f(x) = 0, then you have a true actual root
it might be easier just to go through your answer choices

- anonymous

i would certainly say so!!

- anonymous

huh?

- anonymous

you have choices right? check which ones work

- anonymous

how do i check?

- anonymous

plug in the number

- anonymous

see if you get zero

- anonymous

?

- Nnesha

|dw:1449286024847:dw|
zeros (or x-intercept ) point when graph intersect the x-axis when y=0
so you can substitute given points for x if you get 0 as final answer then that number would be the zero

- anonymous

\[f(1)=3+10-11-10+8=0\] got one on the first try

- anonymous

zeros mean the number that you plug in to get zero out

- anonymous

so if \[f(1)=0\] then "1 is a zero of f"

- anonymous

=0

- anonymous

plug in the numbers, see which give zero
that is all

- anonymous

i dont get it i dont know what to plug in

- jim_thompson5910

Here's one way to generate all the possible rational roots
|dw:1449286106549:dw|
to fill out the table, you compute p/q
eg:
first row, first column = p/q = 1/1 = 1
first row, second column = p/q = 2/1 = 2
etc etc
once the table is filled out, you just put plus/minus in front of each possible root

- jim_thompson5910

sorry I mixed up the two, I meant to say q/p

- jim_thompson5910

@LegendaryNikki if you replaced every x with -1, what result would you get?

- anonymous

i dont know

- Nnesha

what would you do to know ?? :=)
substitute all x for -1 then simplify what would u get ?

- anonymous

ok hold on

- anonymous

f(x)=0

- Nnesha

okay now try 2/3
substitute all x for 2/3
and remember the highest exponent represents the number of solutions(zeros )(including complex , imaginary)

- anonymous

0

- Nnesha

look at the original equation for a sec
what's the highest exponent ?

- anonymous

im confused

- Nnesha

to be honest i don't really like the way *testing each option*
it wouldn't work for all questions
well anyways what you don't understand ? what r you confused about ?

- anonymous

remember the highest exponent represents the number of solutions(zeros )(including complex , imaginary)

- Nnesha

okay what's the highest exponent in that function ??

- anonymous

3

- Nnesha

that's the leading coefficient
i'm asking about exponent

- Nnesha

\[\large \rm Ax^5+Bx^3+C\]
in this example 5 is the highest exponent so there should be 5 solutions

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