3,913 views
7 votes
7 votes
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

1 Answer

Best answer
14 votes
14 votes

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).

selected by
Answer:

Related questions

8 votes
8 votes
3 answers
2
Ishrat Jahan asked Oct 31, 2014
5,000 views
The following definite integral evaluates to$$\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$$$\frac{1}{2}$$\pi \sqrt{10}$$\sqrt{10}$$\pi$
0 votes
0 votes
0 answers
3
2 votes
2 votes
1 answer
4
go_editor asked Dec 10, 2016
547 views
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.