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GATE 2014 CS (CS2) – Question 56

Engineering Mathematics · Calculus · 2 marks · Multiple choice

Newton–Raphson starts at $x_0=2$ for $0.75x^3-2x^2-2x+4=0$. I: $x_3=0$. II: The method converges to a solution in finitely many iterations. Which is TRUE?

  1. Only I
  2. Only II
  3. Both I and II
  4. Neither I nor II

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Correct answer: (A) Only I

Explanation

For f=0.75x³−2x²−2x+4, f(2)=−2 and f′(2)=−1, giving x1=0. At0, f=4,f′=−2, giving x2=2; the cycle repeats, so x3=0. It does not converge to a root. Thus **only I,A**.