11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    If the quadratic equations \[{{x}^{2}}+ax+b=0\]and \[{{\mathbf{x}}^{2}}+\mathbf{bx}+\mathbf{a}=\mathbf{0}\]have a common root then the numerical value of \[\left( \mathbf{a}+\mathbf{b} \right)\] is:

    A)  1                   

    B)  \[-1\]             

    C)  0                                

    D)  2

    Correct Answer: B

    Solution :

    [b] \[\because \alpha \]be the comment roots of the given quadratic equation we have  \[\therefore {{\alpha }^{2}}+a.\alpha +b=0\]                 ??..(1) \[\And {{\alpha }^{2}}+b.\alpha +a=0\]                       ??  (2) (1) ?(2), we have \[\alpha (a-b)+b-a=0\] \[\alpha (a-b)=\left( a-b \right)\] \[\therefore \alpha =1\] Putting these value in the given quadratic equation we have. \[{{1}^{2}}+\alpha .1+b=0\] \[\Rightarrow a+b=-1\] Hence option [b] is correct.

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