M={x|2x^2-x-3>0},N={x|x^2-(k+2)x-6k^2+11k-3<0}满足M∩N≠空集，求实数k的取值范围。希望有详细的过程。谢谢！
热心网友
2x^2-x-30解得x3/2或x3/2或xx2时3k-13-2k即k4/5时所以3k-13/2或3-2k5/6或k2所以k5/6(ⅱ)当x13/2k5/6或k<3/4}
热心网友
要M交N不为空，首先N不能为空，即b^2-4ac=(k+2)^2+4(6k^2-11k-3)或=0本题中b^2-4ac=25k^2-40k-8 恒大于零。计算M中x的范围:(2x-3)(x+1)0 = x3/2N中方程可写为：x^2-(k+2)x-(2k-3)(3k-1)[x-(3k-1)][x+(2k-3)]3k-1,k3/2或3k-19/4或k k-2,则2k-33/2，得k5/6 = -2