Question

I just need someone to check my work.
Use the rational root theorem to list all possible rational roots of the polynomial equation.
x^3+7x2-10x-3

My answers are + or - 1 and + or - 3. Are these right?

Answer 1

what is your equation, please?

Answer 2

The equation is the one on top. x^3+7x^2-10x-3

Answer 3

it is a polynomial only, I don't see the "=" sign

Answer 4

Oh yeah that's it. We're just given the polynomial and have to find the zeros. I'm pretty sure I got the correct answer tho.

Answer 5

Just wanna make sure lol :)

Answer 6

if I set x=1, I get this:
1^3+7*1^2-10*1-3=1+7-10-3=-5 which is not zero
so x=1 can not be a zero of your polynomial

Answer 7

It says to find all the possible zeros. So I'd have to use the rational root theorem and that p over q thing. So the factors of 3 over the factors of 1 and I get + or - 3 and + or - 1. Those would be the POSSIBLE zeros correct?

Answer 8

ok! that's right, your possible values of p/q are \[\pm 1, \quad \pm3\]

Answer 9

Thanks so much! :) Did you get my message btw?

Answer 10

yes! please wait a moment

Answer 11

Ok lol, thanks :)

Answer 12

for your first exercise, you have to check what possible values of p/q satisfy the condition below:
\[P(p/q)=0\]
where P is your polynomial

Answer 13

http://www.sparknotes.com/math/algebra2/polynomials/section4.rhtml

Answer 14

Oh ok, yeah I did use that. There's one question that asks for all the possible values and one where it asks for all the zeros. Thanks tho for checking my work :)

Answer 15

ok! what is your next exercise?

Answer 16

Ok well one of them is:
13) A polynomial equation with rational root coefficients has the roots \[2+\sqrt{4,}\], \[2\sqrt{5}\], find two additional roots. Show all work.

Answer 17

I'm trying...

Answer 18

Alright, thanks so much I really appreciate it. The next question I'll post on a separate thread so I can give you more medals.

Answer 19

Alright! Thank you :)

Answer 20

Sorry, I have made an error! I retry

Answer 21

Oh that's fine :) It's ok.

Answer 22

we can say that your polynomial can be factored as below:
\[P(x)=(x-2\sqrt{5})(x-2-\sqrt{4})*q(x)\]
where q(x) is another polynomial whose degrre is >=2

Answer 23

opps..whose degree is...

Answer 24

Ok... so then I just solve for x?

Answer 25

possible value of p/q are for example:
\[\frac{ 2\sqrt{5} }{ 1 },\frac{ \sqrt{5} }{ 2 }, \frac{ -\sqrt{5} }{ -2 }\]
and so on, but I can not infer that, for example sqrt(5)/2 is a rational root of your equation

Answer 26

Oh ok, yeah that makes sense.

Answer 27

Thanks tho! I'll just plug them in and check :) I really appreciate it :)

Answer 28

thanks! :)
I continue to try