已知方程x²+(m-3)x+m=0,两根都大于3,求m的取值范围
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已知方程x²+(m-3)x+m=0,两根都大于3,求m的取值范围
已知方程x²+(m-3)x+m=0,两根都大于3,求m的取值范围
已知方程x²+(m-3)x+m=0,两根都大于3,求m的取值范围
x1+x2=3-m
x1*x2=m
两根都大于3
则,(x1-3)(x2-3)>0
x1*x2-3(x1+x2)+9>0
m-3(3-m)+9>0
m> 0
且,
(x1-3)+(x2-3)>0
x1+x2-6>0
3-m-6>0
m<-3
综上,m无解