Question 4 (1 mark) Attemp When finding the root of f(x)-0 on the interval [a, b

Question

Question 4 (1 mark) Attemp When finding the root of f(x)-0 on the interval [a, b] using the bisection method we know that f(a) 0. If c is the midpoint of the interval [a, b] and f(c) > 0 then the next step in the bisection method would be? Which statement is correct? A B C D E The product f(c)*f(b) is positive, so we put a = c and go to the next iteration. The product f(c)*f(b) is negative, so we put a = c and go to the next iteration. The product f(c)*f(b) is positive, so we put b = c and go to the next iteration. The product f(c)*f(b) is negative, so we put b = c and go to the next iteration. None of the above

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Kindly note that option B and C are correct since bisection method works on the principle that f(a) and f(b) should be of opposite signs so that f(x) crosses x axis between the interval and there is atleast 1 root to f(x) in the interva.

Next we find the mid value c, and further the sign of f(c) is examined and either (a, f(a)) or (b, f(b)) is replaced with (c, f(c)) so that there is a zero crossing within the new interval.

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