On Products of Delta Distributions and Resultants

We prove an identity in integral geometry, showing that if $P_x$ and $Q_x$ are two polynomials, $\int \mathrm{d}x\, \delta(P_x) \otimes \delta(Q_x)$ is proportional to $\delta(R)$ where $R$ is the resultant of $P_x$ and $Q_x$.