Question

设双元素集合A是方程x平方—4x+m的解集，求实数m的取值范围

Answer 1

假设实数根为x1,x2,有两个不相等实数根
所以5²-4×m
>
0
即
m
<
25/4
|x1-x2|²
=
(x1²-2x1x2+x2²)
=
x1²+2x1x2+x2²
-4x1x2
=(x1+x2)²-4x1x2
=
9
按照根与系数的关系，
x1+x2
=
-5;
x1x2
=
2m
带入上面的式子
(-5)²-4×2m
=
9
25
-
8m
=
9
m
=
2
<
25/4
所以
m
=
2