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BCECE Engineering BCECE Engineering Solved Paper-2014

  • question_answer
    If one of the roots of equation \[{{x}^{2}}+ax\text{ }+\text{3 }=\text{ }0\]  is 3 and one of the roots of the equation \[~{{x}^{2}}+ax+\text{ }b=0\] is three times the other root, then the value of b is

    A)  3                                            

    B) 4      

    C) 2                             

    D) 1

    Correct Answer: A

    Solution :

    Let \[\alpha \]and 3 are the roots of the equation \[{{x}^{2}}+ax+3=0\] \[\therefore \]  \[3\alpha =3\Rightarrow \alpha =1\] and        \[3+\alpha =-a\Rightarrow a=-4\] Again, let \[\beta \]and 3\[\beta \] are the roots of the equation \[{{x}^{2}}+ax+b=0\]. \[\therefore \]  \[\beta +3\beta =-a\]\[\Rightarrow 4\beta =4\]                \[[\because a=-4]\] \[\Rightarrow \]                               \[\beta =1\] and        \[\beta .3\beta =b\Rightarrow 3\times 1=b\Rightarrow b=3\]


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