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VIT Engineering VIT 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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