Maths Question

Could someone explain part b please?
https://i.imgur.com/As5IuWv.jpeg

Reply 1

Could someone explain part b please?
https://i.imgur.com/As5IuWv.jpeg

When the iterative equation in a) converges so x = x_n = x_(n+1) you have
x = -2 -4/x^2
so multiply thorough by x^2 and bring the terms over to the left and you have the cubic in b). So a) is an iterative equation which can be used to approximate a solution of the cubic eqaution.

If you sub -2.6 and -2.64 into b) youll notice that there is a sign change in the left hand side, so there is a root slightly less than -2.6.