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 accurancy of $0.001,$ the required minimum number of iteration is
10

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Solution

The correct option is A 10
In bisection method, the minimum number of iterations is given by $\frac{| b - a |}{2^{n}} < ε$
Where
a: Lower limit of interval
b: Upper limit of interval
$ε$ : Error in approximation
n: Number of iterations
Thus
$\frac{| 2 - 1 |}{2^{n}} < 0.001$
$\Rightarrow$ $2^{n} > 1000$
$\Rightarrow$ $n = 10$

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Only one of the real roots of f(x)=x6−x−1 lies in the interval 1≤x≤2 and bisection method is used to find its value. For achieving an accurancy of 0.001, the required minimum number of iteration is 10

The correct option is A 10In bisection method, the minimum number of iterations is given by |b−a|2n<ε Where a: Lower limit of interval b: Upper limit of interval ε: Error in approximation n: Number of iterations Thus |2−1|2n<0.001 ⇒ 2n>1000 ⇒ n=10

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 accurancy of $0.001,$ the required minimum number of iteration is
10