SILK-ROAD 2008 Problem 4

Find all polynomials $P\in\mathbb{R}[x]$ such that for all $r\in\mathbb{Q}$ ,there exist $d\in\mathbb{Q}$ such that $P(d)=r$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.