Question

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.

Accepted Answer

The correct answer is (B) 3. f(1)=1−1−1−4=−5 (negative), f(9)=6561−729−81−4=5747 (positive). Iteration 1: midpoint 5, f(5)=625−125−25−4=471>0, root narrows to [1,5]. Iteration 2: midpoint 3, f(3)=81−27−9−4=41>0, root narrows to [1,3]. Iteration 3: midpoint 2, f(2)=16−8−4−4=0 exactly — the method has found the exact root x=2 and converges after 3 iterations, matching the file's own answer key.

Explanation