MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## polynomial with no repeated roots [closed]

Suppose I have a polynomial $f$ of degree $d$ having integer coefficients, from $f$ I need to find a polynomial $g$ of degree $\leq d$ whose roots are subset of set of roots of $f$ and $g$ don't share any root with its derivative and double derivative. ie gcd(g,g')=1 and gcd(g,g'')=1

Let me know if there is any doubt regarding the problem.

-
This is not a research-level question. Please check out the FAQ for suggestions of other sites where to ask this question. – Thierry Zell Apr 12 2011 at 11:23
$g=1$ meets your requirements. – Emil Jeřábek Apr 12 2011 at 11:25