Core 1 algebra question that's completely bamboozled me...

Feb 2010
So yeah, I'm looking at C1 past papers for my exam tomorrow, and question 10 part iii to this paper has confused the hell out of me. I understand that you're meant to equate the discriminant of the quadratic to 0, but how do you know that there's only one solution? It's just hurting my brain =/.
Dec 2009

This \(\displaystyle kx-4\) can only be a tangent when the equation \(\displaystyle x^2+x=kx-4\) has exactly one solution, that is, like you stated when the discriminant of \(\displaystyle f(x)=x^2+(1-k)x+4=0\) is equal to zero.

Hence you must find k such that \(\displaystyle \Delta(f) = (1-k)^2-16= 0\)