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GATE | GATE-CS-2014-(Set-2) | Question 56
  • Last Updated : 14 Feb, 2018

In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function


0.75x3 – 2x2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations. 

Which of the following is TRUE?

(A) Only I
(B) Only II
(C) Both I and II
(D) Neither I nor II


Answer: (A)

Explanation: In Newton’s method, we apply below formula to get next value.

 x_{n+1} = x_n - \frac{f{(x_n)}}{f'(x_n)}

f'(x) = 2.25x2 – 4x - 2

x1 = 2 - (0.75*23 – 2*22 – 2*2 + 4)/
         (2.25*22 – 4*2 - 2) 
  = 2 - (-2/-1)
  = 0

x2 = 0 - (4/-2) = 2

x3 = 0

We get x = 0 and x = 2 repeatedly and it never converges.


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