It is given that
$$\begin{aligned}
& \mathrm { f } ( x ) = x ^ { 2 } ( x - 1 ) ^ { 2 } ( x - 2 ) \\
& \mathrm { g } ( x ) = - p ( x - q ) ^ { 2 } ( x - r ) ^ { 2 }
\end{aligned}$$
where $p , q$ and $r$ are positive and $q < r$
Find the set of values of $q$ and $r$ that guarantees the greatest number of distinct real solutions of the equation $\mathrm { f } ( x ) = \mathrm { g } ( x )$ for all $p$.