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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    If the sum of two of the roots of\[{{x}^{3}}+p{{x}^{2}}+qx+r=0\]is zero, then\[pq=\]

    A) \[-r\]                                    

    B) \[2r\]

    C) \[-2r\]                  

    D)        \[r\]

    Correct Answer: D

    Solution :

    Given that,\[\alpha +\beta =0\]              \[\alpha +\beta +\gamma =-p\] \[\Rightarrow \]                            \[\gamma =-p\] Substituting\[\gamma =-p\]in the given equation, \[\Rightarrow \]  \[-{{p}^{3}}+{{p}^{3}}-pq+r=0\] \[\Rightarrow \]                                    \[pq=r\]


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