Question Bank • QB_EM_124 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

In the Bisection method to isolate a real root of $f(x) = 0$ in the initial bracket $[1, 9]$, calculate the minimum number of bisection iterations required to guarantee an absolute error of less than $0.01$.

Answer Key:

10

Step-by-Step Solution & Explanation

The interval length after $n$ iterations is $\frac{b - a}{2^n}$. For error $\le 0.01$: $\frac{9 - 1}{2^n} \le 0.01 \implies \frac{8}{2^n} \le 0.01 \implies 2^n \ge 800$ Since $2^9 = 512$ and $2^{10} = 1024$, the minimum number of iterations is $n = 10$.
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