Functions \(f,g,h\) are defined as follows: \[f:x\mapsto x-4x^{1/2}+1\quad(x\ge0),\] \[g:x\mapsto mx^2+n\quad(x\ge-2),\quad\text{where }m,n\text{ are constants},\] \[h:x\mapsto x^{1/2}-2\quad(x\ge0).\]

(a) Solve the equation \(f(x)=0\), giving your solutions in the form \(x=a+b\sqrt c\), where \(a,b,c\) are integers. [4]

(b) Given that \(f(x)=gh(x)\), find the values of \(m\) and \(n\). [4]