Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
6 votes

Using Newton-Raphson method, a root correct to 3 decimal places of  $x^3 - 3x -5 = 0$

  1. 2.222
  2. 2.275
  3. 2.279
  4. None of the above
in Numerical Methods
edited by

4 Answers

5 votes
Best answer

Answer is (c) 2.279 

selected by
Is there any simple way to solve this type of questions?
how can solve this without calc??

How We started from x0 = 3 ?

x0 is the initial root chosen so that it is closer to the required root..Since the options have positive integers, we can start with numbers 1,2,3 etc..Here,1 and 2 when substituted gives negative answers.And,.To get  xn+1,we use xn+1=xn-[f(xn)/f'(xn)]
8 votes

Shortcut to find an answer to such question in an exam.

Newton-Raphson method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It is one example of a root-finding algorithm.

Here f(x) = x3-3x-5

Just put the options one by one in f(x) and check whether we are getting "0.000..."(correct up to 3 decimal places) as the answer.

op A: x= 2.222   ie. f(x) = (2.222)3-3(2.222)-5 = -0.695354...  // op A is not correct

op B: x= 2.275   ie. f(x) = (2.275)3-3(2.275)-5 = -0.050453...  // op B is not correct

op C: x= 2.279   ie. f(x) = (2.279)3-3(2.279)-5 = -(0.000)236361...  // op C is correct root of given equation (upto 3 decimal places..

So Op C is the answer.

Your approach is easy but calculator is not allowed in ISRO exam..
0 votes
(c) 2.279
0 votes

c) by using this formula Xn+1 = Xn - (f(Xn) / f'(Xn))

f(x)=x3 -3x-5

f(0)= -5<0

f(1)= -7<0

f(2)=  -3<0

f(3)=13 >0

so the real  root should lie between (2,3 )

why is that x0 = 2 cant be taken  ?

Related questions

0 votes
0 answers
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.
asked Nov 9, 2016 in Numerical Methods makhdoom ghaya 276 views
6 votes
1 answer
In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $0.75x^3-2x^2-2x+4=0$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE? Only I Only II Both I and II Neither I nor II
asked Sep 28, 2014 in Numerical Methods jothee 683 views
2 votes
1 answer
Newton-Raphson method is used to compute a root of the equation $x^2 - 13 = 0$ with 3.5 as the initial value. The approximation after one iteration is 3.575 3.676 3.667 3.607
asked Sep 21, 2014 in Numerical Methods gatecse 1.2k views
5 votes
1 answer
The Linux command mknod myfifo b 4 16 will create a character device if user is root will create a named pipe FIFO if user is root will create a block device if user is root None of these
asked May 7, 2017 in Operating System sh!va 4.3k views