Question Bank • QB_EM_GATE_008 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

The Newton-Raphson method is applied to solve $f(x) = x^3 - 2x - 5 = 0$ with $x_0 = 2.0$. The value of $x_1$ after the first iteration is ________ (round off to 3 decimal places).

Answer Key:

2.1

Step-by-Step Solution & Explanation

Newton-Raphson Iteration: $x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2.0 - \frac{2^3 - 2(2) - 5}{3(2^2) - 2} = 2.0 - \frac{-1}{10} = 2.100$ Rounding to 3 decimal places: **2.100**.
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