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 \[\left| \,\begin{matrix}    0 & x & 16  \\    x & 5 & 7  \\    0 & 9 & x  \\ \end{matrix}\, \right|=0\]are [Pb. CET 2001; Karnataka CET 1994]

    A) \[0,\,\,12,\,\,12\]

    B) 0, 12, -12

    C) 0, 12, 16

    D) 0, 9, 16

    Correct Answer: B

    Solution :

    \[\left| \,\begin{matrix}    0 & x & 16  \\    x & 5 & 7  \\    0 & 9 & x  \\ \end{matrix}\, \right|\,=\,0\] By expanding, we get \[-x({{x}^{2}}-144)=0\] \[x=0\] or \[{{x}^{2}}=144\] \[\Rightarrow \] \[x=\pm 12\] So, \[x=0\], \[12,\]\[-12\].


You need to login to perform this action.
You will be redirected in 3 sec spinner