It is given that \[f(x)=(x-2)^2-\lambda(x+1)(x+2).\]

Find the values of \(\lambda\) for which the equation \(f(x)=0\) has two equal roots.

Show that, when \(\lambda=2\), \(f(x)\) has a maximum value of \(25\).

Given that the curve \(y=f(x)\) has a turning point when \(x=\dfrac{1}{4}\), find the value of \(\lambda\) and sketch the curve for this value of \(\lambda\).