# Math Help - Rational Root problem

1. ## Rational Root problem

How is this problem done, and what answers would you get for it?
List all possible rational roots for the function

Give your list in increasing order. Beside each possible rational root, type "yes" if it is a root and "no" if it is not a root. Leave any unnecessary answer blanks empty.

Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .
Possible rational root: Is it a root? .

2. ## You do this

Using the rational root theorem which states that in a function where $p$ is the constant and $q$ is the leading coefficent that after you show ALL the factors of $p$ and $q$ that the only possible rational real roots are all the factors of $p$ over all the factors of $q$ make sense? so in this case you find the factors of p(i.e. 57) which lucky is is a prime so its factors are $\pm$57, $\pm$1 and the factors of $q$ which once again is aprime so the factors are $\pm$3, $\pm$1 now take all the p's over q's

3. Originally Posted by Mathstud28
Using the rational root theorem which states that in a function where $p$ is the constant and $q$ is the leading coefficent that after you show ALL the factors of $p$ and $q$ that the only possible rational real roots are all the factors of $p$ over all the factors of $q$ make sense?
yeah my friend and I tried that and we got imaginary numbers/answers. That why I am also curious what other people got for the answer

4. ## What do you mean

of course there is always the possibility of imaginary roots...but they aren't part of the problem?....wait using Descartes rule of signs there are 4 solutions and they are all real? you must be doing something wrong

5. Originally Posted by Mathstud28
of course there is always the possibility of imaginary roots...but they aren't part of the problem?
thats what me and my friend also got, sorry math is really not my best subject

6. Originally Posted by Girlaaaaaaaa
yeah my friend and I tried that and we got imaginary numbers/answers. That why I am also curious what other people got for the answer
the problem did not ask you to find the roots, there are no real roots. you were asked to list the POSSIBLE rational roots. Mathstud gave you the correct method. Use the rational roots theorem.

so find all the possible roots, and then answer "no" to the "is it a root?" question for every one

7. ## But

you are right this is wrong because all the answers are imaginary...so the question is a trick...you just want the possible roots not the actual ones!

8. Originally Posted by Mathstud28
you are right this is wrong because all the answers are imaginary...so the question is a trick...you just want the possible roots not the actual ones!
would it be then? At least one of the answers above is NOT correct.

(1 pt) List all possible rational roots for the function

Give your list in increasing order. Beside each possible rational root, type "yes" if it is a root and "no" if it is not a root. Leave any unnecessary answer blanks empty.
Those answer were said not to be correct
Possible rational root:-57 Is it a root? .no
Possible rational root: -19 Is it a root? . no
Possible rational root:-1 Is it a root? . no
Possible rational root:-1/3 Is it a root? .no
Possible rational root: 1/3 Is it a root? . no
Possible rational root: 1 Is it a root? . no
Possible rational root: 19 Is it a root? . no
Possible rational root: 57 Is it a root? . no

9. ## All you have to do

is take all your $p$s and $q$s and make them the $\frac{p}{q}$s...that is your answer...none of them are real roots just list the $\frac{p}{q}$s

10. Originally Posted by Mathstud28
is take all your $p$s and $q$s and make them the $\frac{p}{q}$s...that is your answer...none of them are real roots just list the $\frac{p}{q}$s
thats what i did, it did not work I just tried it

11. ## What

what do you mean it didnt work...the numbers didnt divide...you do understand that even if a number is a $\frac{p}{q}$ it doesnt neccasarily have to be a root...all those numbers are possible rational roots...but none of them work in this case