Theoretical Coordinate Geometry

Okay, I came across this question in an old mock paper. The problem is that I couldn't do it and neither could my teacher. Any help would be appreciated.

The line y=2kx cuts the curve $\displaystyle y=x^2-4x+1$ at the points a and b. Without finding the co-ordinates of a and b, find, in terms of k, the midpoint of [ab].

Now I tried putting $\displaystyle 2kx=x^2-4x+1$

and this worked down to $\displaystyle x=2+k \pm \sqrt[2]{k^2+4k+3}$

But I feel that would be finding the co-ordinates of a and b.

Again, any help would be appreciated.