Allied & ICAR Exam Bank • ALLIED_2761 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

The Bisection method for finding roots of $f(x) = 0$ is guaranteed to converge provided:

Options:

  • (A) $f(a) f(b) < 0$ and $f(x)$ is continuous on $[a, b]$
  • (B) $f'(x) \neq 0$
  • (C) $f''(x) > 0$
  • (D) $a > 0$

Answer Key:

A

Step-by-Step Solution & Explanation

By the Intermediate Value Theorem, sign change $f(a)f(b) < 0$ with continuity guarantees at least one root, bracketed by half in each iteration.
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