Construct DFA accepting strings ending with '110' or '101'
There cannot be a single final state. Consider any DFA for the language, and let $\sigma_{110},\sigma_{101}$ be its states after reading $110,101$ (respectively). Clearly $\sigma_{110},\sigma_{101}$ are accepting states. Moreover, they cannot be the same state since $1101$ is in the language but $1011$ is not.