Question

设方程x2+x+m=0的解集为A,方程x2+2mx+m2-m+2=0的解集为B,若A∪B≠∅,求实数m的取值

Answer 1

x^2+x+m=0

△ = 1-4m ≥0

m≤1/4

x^2+2mx+m^2-m+2=0

△ = 4m^2 -4(m^2-m+2)≥0

4m-8 ≥0

m≥2

A∪B≠∅

=>A≠∅ or B≠∅

=> m≤1/4 or m≥2