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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If one of the roots of\[\left| \begin{matrix}    3 & 5 & x  \\    7 & x & 7  \\    x & 5 & 3  \\ \end{matrix} \right|=0\]is\[-10\], then the other roots are

    A)  3, 7                       

    B)         4, 7

    C)  3, 9                       

    D)         3, 4

    Correct Answer: A

    Solution :

    Given,\[\left| \begin{matrix}    3 & 5 & x  \\    7 & x & 7  \\    x & 5 & 3  \\ \end{matrix} \right|=0\] \[\Rightarrow \]               \[3(3x-35)-5(21-7x)+x(35-{{x}^{2}})=0\] \[\Rightarrow \]               \[9x-105-105+35x+35x-{{x}^{3}}=0\] \[\Rightarrow \]               \[{{x}^{3}}-79x+210=0\] \[\Rightarrow \]               \[(x+10)(x-3)(x-7)=0\] \[\Rightarrow \]               \[x=10,\,\,3,\,\,7\]


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