Two remarks on the adjoint polynomial

► We show that the largest real root γ(G) of the adjoint polynomial of a graph G has the largest absolute value among the roots. ► We prove that γ(G)≤4(Δ−1), where Δ denotes the largest degree of the graph G. This bound is sharp. ► We compare the adjoint polynomial with a modified version of the matching polynomial. ► Generating functions arising from the adjoint polynomial are studied.