A) \[-\sqrt{2}\]
B) \[-i\sqrt{3}\]
C) \[i\sqrt{5}\]
D) \[\sqrt{2}\]
Correct Answer: B
Solution :
Let \[\alpha \] be the common root of given equations, then \[{{\alpha }^{2}}+b\alpha -1=0\] ...(1) and \[{{\alpha }^{2}}+\alpha +b=0\] ...(2) Subtracting (2) from (1), we get \[(b-1)\alpha -(b+1)=0\] or \[\alpha =\frac{b+1}{b-1}\] Substituting this value of a in equation (1), we get \[{{\left( \frac{b+1}{b-1} \right)}^{2}}+b\left( \frac{b+1}{b-1} \right)-1=0\] or \[{{b}^{3}}+3b=0\Rightarrow b=0,\] \[i\sqrt{3},\,\,-i\sqrt{3}\]
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