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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
asked in Numerical Methods by Veteran (355k points) | 708 views

1 Answer

+9 votes
Best answer

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).

answered by Boss (11.2k points)
selected by
is it still in the syllabus?
Not in syllabus
okk..thanks buddy!
newton rapson method, simpson or kutta methods, etc What else are not in syllabus. Thanks..

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