(1) As long as it is proved that the discriminant = k 2-4 (k-2) is always greater than 0.

=k^2-4k+8=(k-2)^2+4>； 0

So there are always two sources.

(2) Intersection distance =|x 1-x2|

According to the great theorem

x 1+x2=k

x 1x2=k-2

| x 1-x2 | 2 =(x 1-x2)2 =(x 1+x2)2-4x 1x 2 = k 2-4(k-2)=(k-2)2+。

So k = 2, | x 1-x2 | 2 minimum value =4, |x 1-x2|=2.

The shortest distance between them is 2, and k=2.