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

The discriminant \(\Delta\) is given by \(b^2 - 4ac\).

Here, \(a = 4\), \(b = -24\), and \(c = p\).

So, \(\Delta = (-24)^2 - 4 \times 4 \times p\).

\(\Delta = 576 - 16p\).

For no real roots, \(576 - 16p < 0\).

Solving for \(p\):

\(576 < 16p\)

\(p > 36\)