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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 solutions of the equation \[\left| \,\begin{matrix}    x & 2 & -1  \\    2 & 5 & x  \\    -1 & 2 & x  \\ \end{matrix}\, \right|=0\] are  [Karnataka CET 2005]

    A) \[3,\,\,-1\]

    B) \[-3,\,\,1\]

    C) 3, 1

    D) \[-3,\,\,-1\]

    Correct Answer: A

    Solution :

    \[\left| \,\begin{matrix}    x & 2 & -1  \\    2 & 5 & x  \\    -1 & 2 & x  \\ \end{matrix}\, \right|=0\]Þ\[x(5x-2x)-2(2x+x)-1(4+5)=0\] Þ \[3{{x}^{2}}-6x-9=0,{{x}^{2}}-2x-3=0\],\[(x+1)(x-3)=0\] \[\Rightarrow x=-1,\,3\].


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