Hey everyone,

$\displaystyle I = \{ p \in R[X] : p(1) = p'(1) = 0 \} $

I've got to show that $\displaystyle I$ is a principal ideal in $\displaystyle R[X]$.

If I understand correctly, I've got to find some $\displaystyle q \in R[X]$ for which $\displaystyle qr(1) = qr'(1) = 0$ for any $\displaystyle r \in R[X]$. Is that right?

.. because if it is, I have no clue how to find the answer :(

I'm not asking for the whole solution to the problem, but a little hint would certainly be welcome.

Thank you! :)