A) \[3\]
B) \[4\]
C) \[2\]
D) \[1\]
Correct Answer: A
Solution :
Let \[\alpha \] and 3 are the roots of the equation \[{{x}^{2}}+ax+3=0\]. \[\therefore \] \[3a=3\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\alpha =1\] and \[3+\alpha =-a\] \[\Rightarrow \] \[-a=4\,\,\,\,\Rightarrow \,\,\,\,a=-4\] Again, let \[\beta \] and \[3\beta \] are the roots of the equation \[{{x}^{2}}+ax+b=0\] \[\therefore \] \[\beta +3\beta =-a\] \[\Rightarrow \] \[4\beta =4\,\,\,\Rightarrow \,\,\,\,\beta =1\] and \[\beta .3\beta =b\,\,\,\Rightarrow \,\,\,b=3\]
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