To have the real roots D = b² – 4ac ≥ 0

Here a = 2, b = k and c = 8

D = k² – 4 x 2 x 8 ≥ 0

⇒ K²≥ 64

⇒ K ≥ 8

So for all the values of k greater than or equal to 8 and – 8, the given quadratic equation will have real roots.