∵α、β是方程2X²-5X-2009=0的根∴α+β=5/22β²-5β-2009=02β²-5β=2009∴2β²+6β+11α=2β²-5β+11β+11α=2009+11×(β+α)=2009+11×5/2=2009+55/2=2009+27.5=2036.5