Functions

Consider \(f(x) = 2kx^2 - 4kx + 1\), for \(k \neq 0\). The equation \(f(x) = 0\) has two equal roots.

1. Find the value of \(k\).

   [5]

2. The line \(y = p\) intersects the graph of \(f\). Find all possible values of \(p\).

   [2]