  We consider the coincident root loci consisting of the polynomials with at
least two double roots andpresent a linear basis of the corresponding ideal in
the algebra of symmetric polynomials in terms of the Jack polynomials with
special value of parameter $\alpha = -2.$ As a corollary we present an explicit
formula for the Hilbert-Poincar\`e series of this ideal and the generator of
the minimal degree as a special Jack polynomial.
  A generalization to the case of the symmetric polynomials vanishing on the
double shifted diagonals and the Macdonald polynomials specialized at $t^2 q =
1$ is also presented. We also give similar results for the interpolation Jack
polynomials.
