方程7x2-(m+13)x+m2-m-2=0的两根为x1,x2,且满足0<x1<1,1<x2<2,则m的取值范围为_.

问题描述:

方程7x2-(m+13)x+m2-m-2=0的两根为x1,x2,且满足0<x1<1,1<x2<2,则m的取值范围为______.

设f(x)=7x2-(m+13)x+m2-m-2,则f(x)=0的根满足0<x1<1,1<x2<2,需要:f(0)>0,则m2-m-2>0,解得m>2或m<-1;f(1)<0,则7-(m+13)+m2-m-2<0,解得-2<m<4;f(2)>0,则28-2(m+13)+m2-m-2>0...