11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If the roots of the equation \[{{x}^{3}}-12{{x}^{2}}+39x-28=0\] are in A.P., then their common difference will be [UPSEAT 1994, 99, 2001; RPET 2001]

    A) \[\pm 1\]

    B) \[\pm 2\]

    C) \[\pm 3\]

    D) \[\pm 4\]

    Correct Answer: C

    Solution :

    Let a - d, a, a + d be the roots of the equation \[{{x}^{3}}-12{{x}^{2}}+39x-28=0\] Then \[(a-d)+a+(a+d)=12\] and \[(a-d)\,a\,(a+d)=28\] Þ \[3a=12\]and \[a\,({{a}^{2}}-{{d}^{2}})=28\] Þ \[a=4\] and \[a\,({{a}^{2}}-{{d}^{2}})=28\] Þ \[16-{{d}^{2}}=7\Rightarrow d=\pm \,3\].

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