I will edit to be specific like Shaun said:
If $ax^2+bx+c$ has repeated root $x=r$, what is the condition number solving for $r$ if you only change one of $a,b,c$?
The book says that if $r$ is a simple root that $\kappa= 1/f'(r)$ (but shouldn't this be constant?) but that if the root is repeated that this is ill conditioned but I get $\kappa= 1/(2\sqrt{r} + 2r)$, so how is this enough for it to be ill conditioned? Wouldn't this just be for $r=0$? Or am I doing this wrong?