$x = \dfrac{-\ (-\ 1) \pm \sqrt{(-1)^2 - 4k(-k - 1}}{2k} = \dfrac{1 \pm \sqrt{4k^2 + 4k + 1}}{2k} = \dfrac{1 \pm \sqrt{(2k + 1)^2}}{2k} \implies$

$x = \dfrac{-2k}{2k} = - 1\ or\ x = \dfrac{1 + 2k + 1}{2k} = \dfrac{2k + 2}{2k} = 1 + \dfrac{1}{k}.$

Well done so far.

Notice that the question asks about values (plural) of k. "Uneven" is a bit weird. Normally, one would say odd, which would imply an integer. If "uneven" means "not an even integer," what values of k are acceptable. If "uneven" means an odd integer, what values of k are acceptable. As for part b, notice that one root is negative, what does that imply about k if the other root is positive?