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Matrix polynomials with unitary/doubly stochastic coefficients form thesubject matter of this manuscript. We prove that if $P(\lambda)$ is a quadraticmatrix polynomial whose coefficients are either unitary matrices or doublystochastic matrices, then under certain conditions on these coefficients, thecorresponding block companion matrix $C$ is diagonalizable. Consequently, if$Q(\lambda)$ is another quadratic matrix polynomial with corresponding blockcompanion matrix $D$, then a Hoffman-Wielandt type inequality holds for theblock companion matrices $C$ and $D$.

Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials