  Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary
forms of degree $d$--labelled by partitions of $d$. Given a partition
$\lambda$, let $X_\lambda$ be the set of forms with root multiplicity
corresponding to $\lambda$. There is a natural action of $GL_2(C)$ on
$S^d(C^2)$ and the coincident root loci are invariant under this action. We
calculate their equivariant Poincar\'e duals generalizing formulas of Hilbert
and Kirwan. In the second part we apply these results to present the cohomology
ring of the corresponding moduli spaces (stable points$/G$, semistable
points$/G$, link of the singularity) using geometrically defined relations.
