I've just started year 1 at the university, can't really understand what i have to do, the new signs also confuse me, please guide me and show me how i should handle this question:
i think instead of "k" he ment "n"...
Thanks!
You have to know (and it's easy to prove, but it requires a little abstraction and, perhaps, a little experience in these things) the following:
if $\displaystyle \frac{a}{b}$ is a rational root of the integer polynomial $\displaystyle a_nx^n+a_{n-1}b^{n-1}+...+a_1x+a_0$, then $\displaystyle a\mid a_0\,\,and\,\, b\mid a_n$, with $\displaystyle x\mid y$ meaning "x divides y".
Well, in your case you have $\displaystyle a_0=35^M\,,\,\,a_n=6^N$, so if $\displaystyle \frac{a}{b}$ is a rational root of that pol., it must be that $\displaystyle a\mid 35^M\,\,and\,\,b\mid 6^N\Longrightarrow a\in \pm \{1,5,7,5^2,7^2,...,35, 35^2,...,35^M\}$ $\displaystyle b\in \pm \{1,2,3,2^2,3^2,...,6,6^2,...,6^N\}$
Tonio
ok thank you very much! but i still dont get it, how i suppose to present the solution?? a means the
coefficient of the last part and b is the one for the first part? do i need to divide each value from group
a in each value of group b and find if it's rational root or what?