This thread belongs to the homework section (do not repost though, the moderators will move it).
In order to get help, you need to show some efforts.
I've moved this to the homework section.
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.
What is "Regula Falsi"?
Separate names with a comma.