diophantine

Quartic rationally derived polynomials ★★★

Call a polynomial $p \in {\mathbb Q}[x]$ rationally derived if all roots of $p$ and the nonzero derivatives of $p$ are rational.

Conjecture There does not exist a quartic rationally derived polynomial $p \in {\mathbb Q}[x]$ with four distinct roots.

Posted by mdevos
updated February 16th, 2011