  In the paper we study the distribution of the discriminant $D(P)$ of
polynomials $P$ from the class $\mathcal{P}_{n}(Q)$ of all integer polynomials
of degree $n$ and height at most $Q$. We evaluate the asymptotic number of
polynomials $P\in \mathcal{P}_{n}(Q)$ having all the roots real and satisfying
the inequality $|D(P)|\le X$ as $Q\to\infty$ and $X/Q^{2n-2}\to 0$.
