First question: Find the root of the equation [itex]x^3- 3x+ 1= 0[/itex] by iteration method (six decimal place accuracy).
There are a number of "iteration methods". Are you referring to a particular one? Why don't you select some starting value and show us how you would start the iteration? Also, this equation has 3 real roots. Which one do you mean by "the" root?
Second question: Use the method of Regula Falsi (method of false position) to solve the equation [itex]j(x)= e^x- 3x[/itex]. (Only six iterations are required, accuracy to 4 decimal places.)
First, was this exactly what the problem says? I don't see an equation, just a function- unless "j(x)" has some meaning you didn't mention.