Question

Rational Root Theorm:
x^3 + 9x^2 +15x-114=0

Answer 1

ok rational root theorem says that the "rational roots" have to be of the form
\[\frac{p}{q}\] where p divides the constant and q divides the leading coefficient.

Answer 2

Fundamental Theorem of Algebra,
the Rational Root Theorem,
Descartes' Rule of Signs,
and the Factor Theorem.

Answer 3

since your leading coefficient is 1, that means they will have to be integers that divide 114

Answer 4

So, how i write it? is that's all the working?

Answer 5

\[114=2\times 3\times 19\] so you have a bunch of choices:

\[\{\pm1,\pm2,\pm3,\pm19,\pm114,\pm6,\pm38,\pm57\]

Answer 6

which method is that?

Answer 7

that is finding the possible rational roots

Answer 8

fundamental theorem doesn't say anything about finding the roots, only says that there is one

Answer 9

what study group

Answer 10

you polynomial must have a root in the complex plane

Answer 11

at the top it says openstudy is having study groups. i know nothing about it

Answer 12

because your polynomial is of degree 3 it must have one REAL zero, but it doesn't have to be rational

Answer 13

we should ask saifoo about it
he knows everything

Answer 14

factor theorem says if r is a root of p(x) then
\[p(x)=(x-r)q(x)\] in other words if you know a zero, you can factor

Answer 15

here, im blank!! literally.

Answer 16

any myininaya will have to tell you about descartes rule of sign, because i forget

Answer 17

Sorry sat, im lost again. which one is:

Fundamental Theorem of Algebra,?

the Rational Root Theorem,?

Factor therom?

Answer 18

says something about the possible positive or negative zeros having to do with the change of signs of the coefficients of the polynomial

Answer 19

1) fundamental theorem of algebra: every polynomial has a zero (in the complex plane)

Answer 20

im trying to figure it out from 5 hours now. :(

Answer 21

And where is the working for FTA?

Answer 22

there is no "working" for it. it is just an "existence " theorem. tells you there is one, not how to find it

Answer 23

tell me the exact words which i should write?

Answer 24

rational root theorem is as i described.

Answer 25

\[f(x)=x^3+9x^2+15x-114\]
+ + + -
there is only 1 change so this means there is one possible real root
\[f(-x)=-x^3+9x^2-15x-114\]
- + - -
2 changes so this means there are 2 possible or 0 possible negative real roots

so there could be 1+ and 2- real roots
or
there could be 1+ and 0- real roots which means there is 2 complex roots

Answer 26

"by the fundamental theorem of algebra,
\[x^3 + 9x^2 +15x-114=0\] as a solution in the complex plane."

Answer 27

since the complex zeros come in conjugate pairs, there must be one real zero, since your polynomial has odd degree (it is 3)

Answer 28

ok so one change in sign of
\[p(x)\] means one possible positive root?

Answer 29

that one line is suppose to say possible real root

Answer 30

positive dop

Answer 31

i keep on leaving out the word positive

Answer 32

and two changes of sign of
\[p(-x)\] means 0 or 2 possible negative roots yes?

Answer 33

Is that correct.

Answer 34

yes satellite

Answer 35

@saifoo i listed the possible rational roots for you

Answer 36

we want 3 solutions
so we have two possiblilities
1 positive real +2 negative real+0 complex
1 positive real +0 negative real +2 complex

Answer 37

it is a long list. of course they are only the "possible rational roots" no one guarantees that the roots are rational

Answer 38

If you guys are free, can you help me out?
feel free to decline. i would not mind.
can u guys write me on a doc file and send it here?

we can divide the word among both.

Answer 39

I'm really in a terrible situation now!!

Answer 40

in fact you can check that the one real root is in fact positive and not rational

Answer 41

work*

Answer 42

what do you guys say?

Answer 43

i don't understand
you want us to write what we wrote here but put it in a doc file?

Answer 44

why don't you just copy it down

Answer 45

Yes, this is b/c i can't really copy it from here, it changes it's format.

Answer 46

Let me do a thing, i will type all this what you wrote in doc file and shot it you you guys.. then just let me know if that's correct or not.

Answer 47

i cnt help with the prob but i am here so everyones day just got better!!

Answer 48

give me a minute