in the method -Theory of Fixed Point Iteration of x = g(x)

If the function g(x) has several roots, why sometimes we need to change the form of g(x) to find the other roots?

For example we can have x

^{3}+3x

^{2}+x+4,

one form can be x= -x

^{3}-3x

^{2}-4

or

another form can be

x=sqrt(-x

^{3}-3x

^{2}-4) / sqrt (3)

those two forms converge into diffrent values.WHY?

Thank you

Brad