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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

  • question_answer
    A root of the equation\[\left| \begin{matrix}    0 & x+a & x-b  \\    x+a & 0 & x-c  \\    x+b & x+c & 0  \\ \end{matrix} \right|=0\]is:

    A) \[a\]                                     

    B) \[b\]

    C)  zero     

    D)  1

    Correct Answer: C

    Solution :

    \[0-(x-a)\{0-(x-c)(x+b)\}\] \[+\,(x-b)(x+a)(x+c)=0\] \[(x-a)(x+b)(x-c)\]\[+\,\,(x-b)(x+a)(x+c)=0\] \[2{{x}^{3}}+2acx-2bcx-2abx=0\] \[2x({{x}^{2}}+ac-bc-ab)=0\Rightarrow x=0\]                                


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