  In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$
associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$
considered recently by the first author and M. Zaway. Then we study the
distribution of the zeros of these kernels essentially when $\alpha\in\mathbb
N$ where the zeros are given by the zeros of a real polynomial
$Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.
