  We settle three problems from the literature on stable and real zero
polynomials and their connection to matroid theory. We disprove the weak real
zero amalgamation conjecture by Schweighofer and the second author. We disprove
a conjecture by Br\"and\'en and D'Le\'on by finding a relaxation of a matroid
with the weak half-plane property that does not have the weak half-plane
property itself. Finally, we prove that every quaternionic unimodular matroid
has the half-plane property which was conjectured by Pendavingh and van Zwam.
