  Let $f_1,...,f_s \in \mathbb{K}[x_1,...,x_m]$ be a system of polynomials
generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary
algebraically closed field. Assume that the factor algebra
$\A=\mathbb{K}[x_1,...,x_m]/\I$ is Gorenstein and that we have a bound
$\delta>0$ such that a basis for $\A$ can be computed from multiples of
$f_1,...,f_s$ of degrees at most $\delta$. We propose a method using Sylvester
or Macaulay type resultant matrices of $f_1,...,f_s$ and $J$, where $J$ is a
polynomial of degree $\delta$ generalizing the Jacobian, to compute moment
matrices, and in particular matrices of traces for $\A$. These matrices of
traces in turn allow us to compute a system of multiplication matrices
$\{M_{x_i}|i=1,...,m\}$ of the radical $\sqrt{\I}$, following the approach in
the previous work by Janovitz-Freireich, R\'{o}nyai and Sz\'ant\'o.
Additionally, we give bounds for $\delta$ for the case when $\I$ has finitely
many projective roots in $\mathbb{P}^m_\CC$.
