A) \[-\frac{5}{8}\]
B) \[-\frac{8}{5}\]
C) \[\frac{5}{8}\]
D) \[\frac{8}{5}\]
Correct Answer: D
Solution :
Let \[\alpha \]and \[\beta =-1\]be the roots of the polynomial, then we have \[f(x)={{x}^{2}}+(1-\alpha )x-\alpha \] \[f(1)=2-2\alpha .....i\] \[f(2)=6-3\alpha ......ii\] \[f(1)+f(2)=0\Rightarrow 2-2\alpha +6-3\alpha =0\Rightarrow \alpha =\frac{8}{5}\] So the other root is \[\frac{8}{5}\] So the correct answer is option D.
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