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.