m²x²-(m-3)x+1=0
判别式=[-(m-3)]²-4m²
=m²-6m+9-4m²
=-3m²-6m+9
=-3m²-6m-3+12
=-3(m+1)²+12≤12
所以可能有解
此时-3(m+1)²+12≥0
(m+1)²≤4
-2≤m+1≤2
-3≤m≤1
所以
-3≤m≤1时有解
m<-3,m>1时无解