  For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ we show
that if $f$ belongs to the Laguerre-P\'olya class, and the quotients $q_k :=
\frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots $ satisfy the condition $q_2 \leq
q_3,$ then $f$ has at least one zero in the segment $[-\frac{a_1}{a_2},0].$ We
also give necessary conditions and sufficient conditions of the existence of
such a zero in terms of the quotients $q_k$ for $k=2,3, 4.$
