# Find all polynomials $P(x)$ has $n$ rational roots. [duplicate]

Find all polynomials $P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ such as:

1) $(a_0,a_1,a_2,...,a_n)$ is a permutation of $(0,1,2,...,n)$

2) $P(x)$ has $n$ rational roots.

• Why? Please give some indication of where this question comes from, why it's worth studying, what progress you have made on it, what level of answer you are expecting, etc. Jan 6, 2015 at 15:34
• @GerryMyerson None of that is necessary. This problem is beautiful and that is reason enough.
– Pp..
Jan 6, 2015 at 15:36
• @Pp.., that's reason enough to work on it. It's not reason enough to post an answer. It also doesn't tell us what kind of answer will be appreciated by OP. Jan 6, 2015 at 15:39
• @Pp.., you've been here for 8 days. There are reasons, good reasons, why people here ask for more information when questions are posted with no source, no hint of any effort on the part of the person asking, and no indication of the level of answer expected. Maybe when you've been here a bit longer, you'll have a better understanding of the reasons for this. Jan 6, 2015 at 21:42
• @Pp.. I'm sorry to see that you are so ashamed of your earlier work on this site that you need to disassociate yourself from it by changing your screen name, and I fear it doesn't bode well for your future participation that you choose to hide your identity behind your Pp. Jan 7, 2015 at 16:43