This is a blessed loss. Mate can be forced, but a draw can be achieved under the fifty-move rule.
To probe all KRRPvKQ positions, these tables and their transitive dependencies are also required:
KQRRvKQ · KRRPvK · KRRRvKQ · KRPvKQ · KRRBvKQ · KRRNvKQ · KRRvKQ