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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–Pólya class, and the quotients $$q_k:= \frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots $$ satisfy the condition $$q_2 \le q_3$$, 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 $$k=2,3, 4$$.

On the Closest to Zero Roots and the Second Quotients of Taylor Coefficients of Entire Functions from the Laguerre–Pólya I Class