GATE | GATE CS 2012 | Question 26

The bisection method is applied to compute a zero of the function f(x) = x4 – x3 – x2 – 4 in the
interval [1,9]. The method converges to a solution after ––––– iterations
(A) 1
(B) 3
(C) 5
(D) 7


Answer: (B)

Explanation: In bisection method, we calculate the values at extreme points of given interval, if signs of values are opposite, then we find the middle point. Whatever sign we get at middle point, we take the corner point of opposite sign and repeat the process till we get 0.

f(1) 0
mid = (1 + 9)/2 = 5

f(5) > 0, so zero value lies in [1, 5]
mid = (1+5)/2 = 3

f(3) > 0, so zero value lies in [1, 3]
mid = (1+3)/2 = 2

f(2) = 0

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