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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    If one root of the equation\[lx+mx+n=0\]is\[\frac{9}{2}\] \[(l,m\]and n are positive integers) and\[\frac{m}{4n}=\frac{l}{m},\]then\[l+n\]is equal to

    A)  80           

    B)  85

    C)  90           

    D)  95

    Correct Answer: B

    Solution :

    Given, \[l{{x}^{2}}+mx+n=0\]                    ...(i) Now,  \[D={{m}^{2}}-4nl=0\]   (\[\because \]\[{{m}^{2}}=4ln,\]given) It means roots of given equation are equal. \[\therefore \] \[{{\left( x-\frac{9}{2} \right)}^{2}}=0\] \[\Rightarrow \]       \[4{{x}^{2}}+81-36x=0\]         ...(ii) On comparing Eqs. (i) and (ii), we get \[l=4,m=-36,n=81\] \[\therefore \] \[l+n=4+81=85\]


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