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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If  \[l,m,n\] are real and \[l\ne m\], then the roots of the equation \[(l-m){{x}^{2}}-5(l+m)x-2(l-m)=0\]are [IIT 1979; RPET 1983]

    A) Complex

    B) Real and distinct

    C) Real and equal  

    D) None of these

    Correct Answer: B

    Solution :

    Given equation is  \[(l-m){{x}^{2}}-5(l+m)x-2(l-m)=0\] Its discriminant \[D=25\]\[{{(l+m)}^{2}}+8\]\[{{(l-m)}^{2}}\] which is positive, since \[l,m,n\] are real and \[l\ne m\]. Hence roots are real and distinct.


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