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BCECE Engineering BCECE Engineering Solved Paper-2009

  • question_answer
    If \[\left| \begin{matrix}    x-1 & 5x & 7  \\    {{x}^{2}}-1 & x-1 & 8  \\    2x & 3x & 0  \\ \end{matrix} \right|=a{{x}^{3}}+b{{x}^{2}}+cx+d,\]then c is equal to

    A) \[-1\]                    

    B)         12                         

    C)  15                         

    D)         17

    Correct Answer: D

    Solution :

    Given, \[\left| \begin{matrix}    x-1 & 5x & 7  \\    {{x}^{2}}-1 & x-1 & 8  \\    2x & 3x & 0  \\ \end{matrix} \right|=a{{x}^{2}}+b{{x}^{2}}+cx+d\] LHS\[=(x-1)(0-24x)-5x(0-16x)\] \[+\,7(3{{x}^{2}}-3x-2{{x}^{2}}+2x)\] \[=-24{{x}^{2}}+24x+80{{x}^{2}}+21{{x}^{3}}-14{{x}^{2}}-7x\] \[=21{{x}^{3}}+42{{x}^{2}}+17x\] \[\therefore \]  \[21{{x}^{3}}+42{{x}^{2}}+17x\] \[=a{{x}^{3}}+b{{x}^{2}}+cx+d\]                 \[\Rightarrow \]               \[c=17\]                


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