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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If\[f(x)=2{{x}^{4}}-13{{x}^{2}}+ax+b\]is divisible by\[{{x}^{2}}-3x+2\], then\[(a,\,\,b)\]is equal to

    A)  (-9,-2)        

    B)                         (6, 4)

    C)  (9, 2)                    

    D)         (2, 9)

    Correct Answer: C

    Solution :

    Given,\[f(x)=2{{x}^{4}}-13{{x}^{2}}+ax+b\]is divisible by\[(x-2)(x-1)\]. \[\therefore \]  \[f(2)=2{{(2)}^{4}}-13{{(2)}^{2}}+a(2)+b=0\] \[\Rightarrow \]               \[2a+b=20\]                                       ... (i) and\[f(1)=2{{(1)}^{4}}-13{{(1)}^{2}}+a+b=0\] \[\Rightarrow \]               \[a+b=11\]                                          ... (ii) On solving Eqs. (i) and (ii), we get                 \[a=9,\,\,b=2\]


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