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

Feb 2010
34
3
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
411
131
Indeed,

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 \(\displaystyle \Delta(f) = (1-k)^2-16= 0\)