Question

已知集合m={x‖x²-3x+2≦0},n={x‖x>0},则

设集合M={x\x2-3x+2=0},N={x|2x2+2x+k=0}不等于空集,若M交N等于空集,求k的取值范围?

Answer 1

M={x\x2-3x+2=0}={1,2}
∵N≠Φ, M交N等于空集
∴2x2+2x+k=0（#）中
Δ=4-8k≥0 ==>k≤1/2
且1,2均不是（#）的解
∴ 2+2+k≠0 ==>k≠-4
8+4+k≠0 ==>k≠-12
∴k的取值范围是k≤1/2且k≠-12且k≠-12