A) \[-2.125\]
B) \[2.125\]
C) \[-2.812\]
D) \[~2.812\]
Correct Answer: A
Solution :
We know that, the first approximation by the method of false position is \[{{x}_{2}}={{x}_{0}}-\frac{{{x}_{1}}-{{x}_{0}}}{f({{x}_{1}})-f({{x}_{0}})}f({{x}_{0}})\] where \[{{x}_{0}}=-3,\,{{x}_{1}}=-2,\] \[f(x)={{x}^{3}}-3x+4\] \[\therefore \] \[f({{x}_{0}})=f(-3)=-27+9+4=-14\] \[f({{x}_{1}})=f(-2)=-8+6+4=2\] Thus, \[{{x}_{2}}=-3-\frac{1}{16}.(-14)\] \[\Rightarrow \] \[{{x}_{3}}=-3+\frac{7}{8}\] \[\Rightarrow \] \[{{x}_{2}}=-\frac{17}{8}\] \[\Rightarrow \] \[{{x}_{2}}=-2.125\]
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