已知集合A={x|x²-4mx+2m+6=0,x∈R},B+{x|x＜0,x∈R}.若A与B中有相同元素,求实数m的取值范围
人气：103 ℃ 时间：2020-05-08 15:40:45
解答
题意为：方程x²-4mx+2m+6=0在(-∞,0)上有解、
△=16m^2-4(2m+6)=8(2m^2-m-3)=8(m+1)(2m-3)≥0
m≤-1或m≥3/2
若在(-∞,0)上有1个解,
△≥0
x1x2=2m+60
x1+x2=4m0
解得-3
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