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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    If one root of the equation \[{{x}^{2}}+px+q=0\]is \[2+\sqrt{3},\] then the value of p and q are

    A)  \[-4,1\]          

    B)  \[4,-1\]

    C)  \[2,\,\,\,\sqrt{3}\]         

    D)  \[-2,-\,\,\,\sqrt{3}\]

    Correct Answer: A

    Solution :

    Since, one root of the equation \[{{x}^{2}}+px+q=0\] is \[2+\sqrt{3},\] then the other root will be \[2-\sqrt{3}\]. \[\therefore \] Sum of roots,  \[2+\sqrt{3}+2-\sqrt{3}=-p\] \[\Rightarrow \] \[4=-p\] \[\Rightarrow \] \[p=-4\] and product of roots \[(2+\sqrt{3})(2-\sqrt{3})=q\] \[\Rightarrow \]\[1=q\] Hence, required values of p and q are \[-4\] and respectively.


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