Question

设函数f(x)=x方+(m-4)x-6m方-2m+4,已知f(a)=f(b)=0,且a、b均大于1,求m范围

Answer 1

解析：原题目等价于方程x^2+(m-4)x-6m^2-2m+4=0的两根都大于1,

∴△=（m-4)^2-4(-6m^2-2m+4)=25m^2≥0,

a+b=4-m,ab=-6m^2-2m+4

(a-1)+(b-1)=a+b-2=2-m＞0

(a-1)(b-1)=ab-(a+b)+1=-6m^2-2m+4-4+m+1

=-6m^2-m+1＞0

解之m＜2,且-1/2＜m＜1/3

∴-1/2＜m＜1/3