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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    When \[({{x}^{3}}-2{{x}^{2}}+px-q)\] is divided by \[({{x}^{2}}-2x-3),\]the remainder is\[(x-6).\]The values of p and q respectively are

    A)  -2,-6                            

    B)  2,-6                 

    C)  -2, 6                

    D)         2, 6                 

    Correct Answer: C

    Solution :

    Let \[f(x)={{x}^{3}}-2{{x}^{2}}+px-q\] and \[g(x)={{x}^{2}}-2x-3=(x-3)(x+1)\] Now, when \[g(x),\]leaves a remainder \[(x-6).\] Then, we have, \[f(3)=x-6\]and\[f(-1)=x-6\] \[\Rightarrow \]\[27-18+3p-q=3-6\] and \[-1-2-p-q=-1-6\] \[\Rightarrow \]\[3p-q=-12\]                                              ?(i) and \[p+q=4\] Adding (i) and (ii), we get                         ?(ii) \[4p=-8\Rightarrow p=-2\] and \[q=3(-2)+12=-6+12=6\]


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