By Bolzano's Theorem there is a solution in . Choose and construct the corresponding sequence.
Surely you are not expecting people to do this problem for you. Show what you have done. Of course, Newton-Raphson is an iterative method- for each approximation, , to the solution of f(x)= 0, should be a better approximation and, hopefully, the sequence will converge to a solution.
for an equation like this ...
newton raphson iterative scheme is given by
for the given equation f(x)=
first we find the location of the root by the method of tabulation . .
the table for f(x) is
x 0 1 2 3 4
f(x) -4 -13 -12 -1 28
the positive root is near x = 3
we take in newton raphson iterative scheme
we get ,
similarly ,
and
thus , the positive root is 3.0514 , correct to five significant digits