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SSC Sample Paper Mock Test-10 SSC CGL Tear-II Paper-1

  • question_answer
    If \[(x+2)\] is the HCF of \[{{x}^{2}}+ax+b\] and \[{{x}^{2}}+cx+d\]\[(a\ne c\,\,\text{and}\,\,b\ne d),\] then which one of the following is correct?

    A)  \[a+c=b+d\]

    B)         \[2a+b=2c+d\]

    C)  \[b+2c=2a+d\]

    D)  \[b-2c=2a-d\]

    Correct Answer: C

    Solution :

    Let \[f\,\,(x)={{x}^{2}}+ax+b\] and \[g\,\,(x)={{x}^{2}}+cx+d\] \[\therefore \]      \[f\,\,(-\,\,2)=4-2a+b=0\] \[\Rightarrow \]   \[b-2a=-\,\,4\] and       \[g\,\,(-\,\,2)=4-2c+d=0\] \[\Rightarrow \]   \[d-2c=-\,\,4\] \[\therefore \]      \[b-2a=d-2c\] \[\Rightarrow \]   \[b+2c=d+2a\]


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