Let $P_n(t)$ be polynomials with integer coefficients with $d_n = \deg(P_n(t))$ going to infinity when $n$ goes to infinity and with nonzero discriminants $disc(P_n(t)) \neq 0$.
Question: Is $$\lbrace disc({P_n(t)})\rbrace ^{\frac{1}{d_n}}$$ bounded when $n$ goes to infinity ?