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10th Class Mathematics Related to Competitive Exam Question Bank Algebra

  • question_answer
    If \[x+2\] is factor of \[{{\{{{(x+1)}^{5}}+2x+K)}^{3}}\}\], then the value of 'K' is

    A)  1                            

    B)         3

    C)  4                            

    D)         5  

    Correct Answer: D

    Solution :

     If \[x+2\] is a factor of\[f(x)={{(x+1)}^{5}}+{{(2x+K)}^{3}}\], then                 \[f(-2)=0\] or            \[{{(-2+1)}^{5}}+{{[2\times (-2)+K]}^{3}}=0\] or            \[-1+{{(K-4)}^{3}}=0\] or            \[[(K-4)-1]{{(K-4)}^{2}}+1+(K-4)]=0\] or            \[K=1\], as\[[{{(K-4)}^{2}}+1+(K-4)]\]does not give real value of\[K\].


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