已知函数y=(x^2+mx+3)/(x+n)的值域是(-oo,-2]U[4,+oo),求m,n

来源：百度知道 编辑：UC知道 时间：2024/05/24 08:51:32
快 详细些
kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

已知函数y=(x^2+mx+3)/(x+n)的值域是(-oo,-2]U[4,+oo)

由于函数次数小于3，故最大值点和最小值点都只有1个

当
y=-2时
x^2+mx+3=-2x-2n
x^2+(m+2)x+(3+2n)=0
判别式=（m+2）^2-4(3+2n)
=m^2+4m+4-12-8n=m^2+4m-8n-8=0.....(1)

当
y=4时
x^2+mx+3=4x+4n
x^2+(m-4)x+(3-4n)=0
判别式=（m-4）^2-4(3-4n)
=m^2-8m+16-12+16n=m^2-8m+16n+4=0....(2)

联立（1），（2）
m=2n+1
n=1/2或-3/2
m=2或m=-2