2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69352Let $f_1$ and $f_2$ be two semi-universal deformations of quasi homogeneous polynomials in two variables respectively for the weight vectors $ρ_1$ and $ρ_2$ such that they satisfy similar conditions to that of semi quasi homogeneous singularities for one weight. By methods inspired by H. Maynadier's, we give an explicit formula for a Bernstein-Sato polynomial involving two affine forms $ρ_i(f_1) s_1 + ρ_i(f_2) s_2 +k$, $i=1,2$. In the particular case $(f_1, f_2)=(x_1^a+x_2^b, x_1^c+x_2^d)$, we calculate the space $\mathcal{H}_f$ recently studied by J. Briançon, Ph. Maisonobe and M. Merle and we show that it is equal to the zero set of $s_1 s_2 (ab s_1+ ad s_2)(ad s_1+ cd s_2)$.in french, 17 pages, no figures. Accepted version in Kyushu J. MathRings and AlgebrasComplex Variables16S32; 32C38text