Let $\xi_0,\xi_1,\dots,\xi_n,\dots$ be a sequence of independent identically distributed random variables, $N_n$ be the number of real roots of the polynomial $\sum_{j=0}^n\xi_jx^j$ . The main result is Theorem 1.{\em If$\mathbf P\{\xi_j=0\}=0$,$\mathbf E\xi_j=0$,$\mathbf E|\xi_j|^{2+s}<\infty$for some positive number$s$, then}$$ \mathbf DN_n\sim4\biggl(\frac1\pi-\frac2{\pi^2}\biggr)\ln n\quad(n\to\infty). $$