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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    The roots of the equation \[\left| \,\begin{matrix}    x & 0 & 8  \\    4 & 1 & 3  \\    2 & 0 & x  \\ \end{matrix}\, \right|=0\]are equal to  [Pb. CET 2000]

    A) \[(-4,\,4)\]

    B) \[(2,\,-4)\]

    C) \[(2,\,4)\]

    D) \[(2,\,8)\]

    Correct Answer: A

    Solution :

    We have \[\left| \,\begin{matrix}    x & 0 & 8  \\    4 & 1 & 3  \\    2 & 0 & x  \\ \end{matrix}\, \right|\,=0\] \[\therefore \]  \[\Delta =x(x-0)-0(4x-6)+8(0-2)\] or \[{{x}^{2}}-16=0\] \[\Rightarrow \] \[x=4,\,-4\].


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