GATE 2025 BM – Question 57
Engineering Mathematics · Numerical Methods · 2 marks · Numerical answer
Use one Newton–Raphson iteration for x³−2x−5=0 from x0=3. Give x1 to two decimal places.
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Show answer and explanation
Correct answer: 2.30 to 2.40
Explanation
Let f=x³−2x−5 and f′=3x²−2. At x=3, f=16 and f′=25. Thus x1=3−16/25=3−0.64=2.36, the requested first iterate rather than the fully converged root.
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