One root of $x^{2} + kx – 8 = 0$ is square of the other. Then, the value of k is:

Let the roots of the quadratic equation be α and α^{2}.

Product of roots = α*α^{2} = -8

α^{3} = -8

α = -2

Roots are -2 and 4 , now put the roots in given equation

4^{2} + 4k - 8 = 0

k = -2

Option D is Correct.