Odd, that's pretty much what the Muslim extremists are saying, except they want to kill the "unbelievers".
I'm unable to find an example in history where committing genocide has helped anyone actually solve problems. It seems what goes around, comes around.
Perhaps a more reasoned solution is in order, like just going after anyone who would commit murder to further their ends. Note that killing terrorists is not murder, but killing noncombatants is.
Imal
Not that I approve, but genocide of the Woodlands Indians solved a lot of problems for the early US government. It opened up Ohio for settlement and helped the state govt's concerning land warrants issued for service in the Revolutionary War.