11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer
    If \[(x+1)\] is a factor of\[{{x}^{4}}-(p-3){{x}^{3}}-(3p-5){{x}^{2}}\] \[+(2p-7)x+6\], then \[p=\] [IIT 1975]

    A) 4

    B) 2

    C) 1

    D) None of these

    Correct Answer: A

    Solution :

    If \[(x+1)\] is a factor of \[{{x}^{4}}-(p-3){{x}^{3}}-(3p-5){{x}^{2}}+(2p-7)x+6\] , then by putting\[x=-1\], we get \[1+(p-3)-(3p-5)-(2p-7)+6=0\] Þ \[-4p=-16\,\,\,\Rightarrow p=4\].

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