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GATE 2026 ME – Question 14

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 1 mark · Multiple choice

Newton-Raphson method for solving algebraic equations is based on

  1. Taylor series
  2. Fourier series
  3. Laurent series
  4. Power series

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Show answer and explanation

Correct answer: (A) Taylor series

Explanation

The method approximates $f(x)$ near the current guess by the first two terms of its Taylor series, $f(x_0) + f'(x_0)(x - x_0)$, and sets this to zero to get the next guess.