设二个交点坐标是(x1,0),(x2,0)
x1+x2=-a
x1x2=a-2
|x1-x2|^2=(x1+x2)^2-4x1x2
(2根号5)^2=a^2-4(a-2)
a^2-4a-12=0
(a-6)(a+2)=0
a=6或-2