root-finding

Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places) is ______________

A numerical solution of the equation $$f\left( x \right) = x + \sqrt x - 3 = 0$$ can be obtained using Newton $$-$$ Raphson method. If the starting values is $$x=2$$ for the iterat...

The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is

The equation $${x^3} - {x^2} + 4x - 4 = 0\,\,$$ is to be solved using the Newton - Raphson method. If $$x=2$$ taken as the initial approximation of the solution then the next appro...