If the roots of the quadratic equation $x^2-2kx+k^2-1=0$ lie in the interval $(–4, 5)$, how to find the sum of all possible values of $\lfloor {k} \rfloor$?
Attempt:
$ x^2-2kx+k^2-1=0$ $\Rightarrow (x-k)^2=1 $ $\Rightarrow k=x \mp 1$
From this we could say that $k \in (-3,6)$ when $k=x+1$ and $k \in (-5,4)$ when $k=x-1$, but then how to do the rest?