Let $r > 1$, $\epsilon > 0$, $\eta > 0$ does there always exist a monic polynomial with integer coefficients $P$ such that
- $P$ has a unique real root $r_0$, s.t $|r_0 - r| < \epsilon$
- For all other roots of $P$, $r_i$, $|r_i| < \eta$
(I'm expecting this to be false)