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The bisection method is applied to compute a zero of the function $f(x) =x ^{4} – x ^{3} – x ^{2} – 4$ in the interval [1,9]. The method converges to a solution after ––––– iterations.

(A) 1
(B) 3
(C) 5
(D) 7

Bisection method is exactly like binary search on a list.

In bisection method, in each iteration, we pick the mid point of the interval as approxiamation of the root, and see where are we, i.e. should we choose left sub-interval, or right-subinterval, and we continue until we find the root, or we reach some error tolerance.

So in first iteration, our guess for root is mid point of [1,9] i.e. 5. Now f(5) > 0, so we choose left sub-interval [1,5] (as any value in right sub-interval [5,9] would give more positive value of $f$).

In second iteration, we choose mid point of [1,5] i.e. 3, but again f(3) > 0, so we again choose left sub-interval [1,3].

In third iteration, we choose mid point of [1,3] i.e. 2, now f(2) = 0

So we found root in 3 iterations. So answer is option (B).

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is it still in the syllabus?
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Not in syllabus
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okk..thanks buddy!
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newton rapson method, simpson or kutta methods, etc What else are not in syllabus. Thanks..

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