Noncoercive sums of squares in R[x1,…,xn]R[x1,…,xn]

Positive definite forms f∈R[x1,…,xn]f∈R[x1,…,xn] which are sums of squares of forms of R[x1,…,xn]R[x1,…,xn] are constructed to have the additional property that the members of any collection of forms whose squares sum to ff must share a nontrivial complex root in CnCn.