For the quadratic equation \(ax^2 + bx + c = 0\) to have no real roots, the discriminant must be less than zero: \(b^2 - 4ac < 0\).

Here, \(a = 8\), \(b = k\), and \(c = 2\).

Substitute these values into the discriminant condition:

\(k^2 - 4 \times 8 \times 2 < 0\)

\(k^2 - 64 < 0\)

\(k^2 < 64\)

This implies \(-8 < k < 8\).