For a commutative hypergroup \(K\), the support \(\text{supp} \pi\) of the Plancherel measure is usually a proper subset of the dual space \(\widehat K\), and it is an open problem whether \(1\in\text{supp} \pi\) implies \(\text{supp} \pi=\widehat K\). The authors of this note under review suggest the related conjecture that the symmetry of \(K\) (i.e., all bounded multiplicative functions are Hermitian) implies \(\text{supp} \pi=\widehat K\). This conjecture is supported by the following main result of the paper: Each symmetric one-dimensional polynomial hypergroup satisfies \(\widehat K \subset [\inf \text{supp} \pi, \sup \text{supp} \pi]\) (where \(\widehat K\) is regarded as usual as a subset of the real line).