A) \[{{b}^{2}}-b=42\]
B) \[{{b}^{2}}-b=30\]
C) \[{{b}^{2}}+b=12\]
D) \[{{b}^{2}}+b=72\]
Correct Answer: B
Solution :
As \[b\in R\] let roots be \[\alpha \pm i\beta \] \[\Rightarrow 2\alpha =-b\] and \[{{\alpha }^{2}}+{{\beta }^{2}}=45\] Also \[\left| \alpha +i\beta +1 \right|=2\sqrt{10}\] \[\Rightarrow {{(\alpha +1)}^{2}}+{{\beta }^{2}}=40\] \[\Rightarrow 45+2\alpha +1=40\] \[\alpha =-3\] and \[b=6\] \[\Rightarrow {{b}^{2}}-b=30\]
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