Allied & ICAR Exam Bank • ALLIED_2758 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

Using the Newton–Raphson method, the root of $f(x) = x^2 - 5 = 0$ starting with initial guess $x_0 = 2$ after one iteration ($x_1$) is:

Answer Key:

2.25

Step-by-Step Solution & Explanation

$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2 - \frac{2^2 - 5}{2(2)} = 2 - \frac{-1}{4} = 2 + 0.25 = 2.25$.
← Previous (ALLIED_2757) Next (ALLIED_2759) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test