  Let \begin{equation*} A_{q}^{(\alpha)}(a;z) = \sum_{k=0}^{\infty}
\frac{(a;q)_{k} q^{\alpha k^2} z^k} {(q;q)_{k}}, \end{equation*} where $\alpha
>0,~0<q<1.$ In a paper of Ruiming Zhang, he asked under what conditions the
zeros of the entire function $A_{q}^{(\alpha)}(a;z)$ are all real and
established some results on the zeros of $A_{q}^{(\alpha)}(a;z)$ which present
a partial answer to that question. In the present paper, we will set up some
results on certain entire functions which includes that
$A_{q}^{(\alpha)}(q^l;z),~l\geq 2$ has only infinitely many negative zeros that
gives a partial answer to Zhang's question. In addition, we establish some
results on zeros of certain entire functions involving the Rogers-Szeg\H{o}
polynomials and the Stieltjes-Wigert polynomials.
