After research, the conclusion is the formula is useful only if you know the real root (the final answer).

According to Pelangi book (wrong)

If is an approximation to a root of the equation , then sequence defined by with a starting value close to will converge to as long as .

The Real

If is a real root of the equation , then sequence defined by with a starting value close to will converge to as long as .

I am not going to describe the proving in details. For more details, check here.

Sample Question from school mock exam

Question

Solution given by the teacher

Solution a

Solution b

Seriously, i wont suggest students to write this working in STPM exam. Even the F'(x) is more than 1, where x is the first estimate, the iterations still converge to the root in different situation. I will recommend sketched graph method.

Solution c

Seriously, i wont suggest students to write this working in STPM exam. Even the F'(x) is more than 1, where x is the first estimate, the iterations still converge to the root in different situation. I will recommend sketched graph method.

Solution d