GATE 2017 EE – Question 52
Only one of the real roots of $f(x) = x^6 - x - 1$ lies in the interval $1 \leq x \leq 2$ and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________.
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Correct answer: 10 to 10
Explanation
Each bisection halves the interval, so after $n$ iterations the interval has length $\frac{2 - 1}{2^n}$. For an accuracy of 0.001 we need $\frac{1}{2^n} \leq 0.001$, which means $2^n \geq 1000$. Since $2^{10} = 1024$, the minimum number of iterations is 10.