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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If the factors of\[{{a}^{2}}+{{b}^{2}}+2(ab+bc+ca)\]are\[(a+b+m)\]and\[(a+b+nc)\], find the value of\[m+n\].

    A) \[0\]                 

    B)        \[2\]                 

    C) \[4\]                 

    D)        \[6\]                 

    Correct Answer: B

    Solution :

    \[{{a}^{2}}+{{b}^{2}}+2ab+2bc+2ca+{{c}^{2}}-{{c}^{2}}\] \[={{(a+b+c)}^{2}}-{{c}^{2}}\] \[=(a+b)(a+b+2c)\] On comparing with \[(a+b+m)(a+b+nc),\] We get \[m=0\]and \[n=2.\] \[\Rightarrow \]\[m+n=0+2=2\]


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