Allied & ICAR Exam Bank • ALLIED_0105 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 a real root is guaranteed to converge if:

Options:

  • (A) $f(a) \cdot f(b) < 0$ for continuous $f(x)$ on $[a, b]$
  • (B) $f'(x) \ne 0$ everywhere
  • (C) $f''(x) > 0$
  • (D) The initial guess is positive

Answer Key:

A

Step-by-Step Solution & Explanation

By the Intermediate Value Theorem, if $f(a)$ and $f(b)$ have opposite signs and $f$ is continuous, a root exists in $[a, b]$.
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