函数y=x2+mx+2与函数y=x+1(0<=x<=2)的图象有公共点,求实数m的取值范围/
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2011-08-13
展开全部
x2+mx+2=x+1(0<=x<=2)有根 f=x²+(m-1)x+1=0在[0,2]有解
△>=0 (m-1)²-4>=0 m>=3或m<=-1
1 f(0)f(2)<=0 1*[4+2(m-1)+1]<=0 m<-3/2
2 f(0)f(2)>=0 且0<=(1-m)/2<=2 -3/2<=m<=1
所以-3/2<=m<=-1
△>=0 (m-1)²-4>=0 m>=3或m<=-1
1 f(0)f(2)<=0 1*[4+2(m-1)+1]<=0 m<-3/2
2 f(0)f(2)>=0 且0<=(1-m)/2<=2 -3/2<=m<=1
所以-3/2<=m<=-1
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