A) 9/15
B) 3
C) 11/5
D) 19/5
Correct Answer: C
Solution :
Given, \[f(x)={{x}^{2}}-x-2\] \[\Rightarrow \] \[f'(x)=2x-1\] By Newton, Raphson method, \[{{x}_{1}}={{x}_{0}}-\frac{f({{x}_{0}})}{f'({{x}_{0}})}\] \[\Rightarrow \] \[{{x}_{1}}=1-\frac{f(1)}{f'(1)}\] \[\Rightarrow \] \[{{x}_{1}}=1-\frac{(1-1-2)}{2-1}=3\] and \[{{x}_{2}}={{x}_{1}}-\frac{f({{x}_{1}})}{f'({{x}_{1}})}\] \[\Rightarrow \] \[x=3-\frac{(9-3-2)}{(2\times 3-1)}\] \[\Rightarrow \] \[{{x}_{2}}=\frac{11}{5}\]
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