GATE 2024 MN – Question 52
Apply two bisection iterations on[0, 1] to $f(x)=x^3-2x^2+3x-1$. Give the root estimate to two decimals.
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Correct answer: 0.25 to 0.50
Explanation
The first midpoint is 0.5, where f=0.125>0, so retain[0, 0.5]. The second midpoint is 0.25, where f=−0.359375<0, so retain[0.25, 0.5]. The second tested estimate is 0.25; the midpoint of the final bracket is 0.375≈0.38. Both fall in the source’s accepted 0.25–0.50 range; the iteration convention is made explicit.