Consider a random polynomial GQ (x) = ξQ,n xn + ξQ,n−1 xn−1 + · · · + ξQ,0 with independent coefficients that are uniformly distributed on 2Q+1 integer points {−Q, …, Q}. Denote by D(GQ) the discriminant of GQ. We show that there exists a constant Cn depending on n only such that for all Q ≥ 2, the distribution of D(GQ) can be approximated as follows: (Formula presented) where ϕn denotes the probability density function of the discriminant of a random polynomial of degree n with independent coefficients that are uniformly distributed on [−1, 1]. Let Δ(GQ) denote the minimal distance between complex roots of GQ. As an application, we show that for any ε > 0 there exists a constant δn > 0 such that Δ(GQ) is stochastically bounded from below/above for all sufficiently large Q in the following sense: (Formula presented) Bibliography: 14 titles.