here is one solution to the problem....

there is one more solution...Rxf7...and then either king has to capture rook else he can't move and he has to move his pawn...so if black plays  Kxf7 or moves his pawn then Qf8# will solve problem.

Another solution is:

1. Q-b5,

then black must either:

block with Q to d7 at which point wQxQ which is mate;or move K to e7 then white queen to d7 is mate