Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations

A curve is defined by the equation:

\(\mathrm{f}\left( x \right)=k\left( {{x}^{2}}-4x \right)\), \(x\in \mathbb{R}\),

where \(k\) is a positive constant. The equation \(\left| \mathrm{f}\left( x \right) \right|=12\) has three distinct roots.

1. Determine the value of \(k\).
2. Find the three roots of the equation, in exact surd form where appropriate.