  We give an example of a function $f$ non-vanishing in the closed bidisk and
the affine polynomial minimizing the norm of $1-pf$ in the Hardy space of the
bidisk among all affine polynomials $p$. We show that this polynomial vanishes
inside the bidisk. This provides a counterexample to the weakest form of a
conjecture due to Shanks that has been open since 1980, with applications that
arose from digital filter design. This counterexample has a simple form and
follows naturally from [7], where the phenomenon of zeros seeping into the unit
disk was already observed for similar minimization problems in one variable.
