x^2+2(m-1)x+3m^2=11
x^2+2(m-1)x+3m^2-11=0
x1=-(m-1)+((m-1)^2-3m^2+11)^0.5=-(m-1)+(m^2-2m+1-3m^2+11)^0.5=-(m-1)+(-2m^2-2m+12)^0.5
x2=-(m-1)-((m-1)^2-3m^2+11)^0.5=-(m-1)-(m^2-2m+1-3m^2+11)^0.5=-(m-1)-(-2m^2-2m+12)^0.5
1.有两个不等实数根
-2m^2-2m+12>0,(2m+6)(-m+2)>0
2>m>-3
2.有两个相等实数根：
-2m^2-2m+12=0,2m^2+2m-12=0,(2m+6)(m-2)=0
m=-3或m=2
3.无实数根
-2m^2-2m+120
2>m>-3
5.有两个正实数根
-2m^2-2m+12>=0,(2m+6)(-m+2)>=0
2>=m>=-3