2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Complex Numbers and Quadratic Equations

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

  • question_answer
    If the equation \[(m-n){{x}^{2}}+(n-l)x+l-m=0\] has equal roots, then l, m and n satisfy [DCE 2002]

    A) \[2l=m+n\]

    B) \[2m=n+l\]

    C) \[m=n+l\]

    D) \[l=m+n\]

    Correct Answer: B

    Solution :

    Roots are equal so \[{{b}^{2}}-4ac=0\] Þ \[{{(n-l)}^{2}}-4(m-n)(l-m)=0\] Þ  \[{{n}^{2}}+{{l}^{2}}-2nl-4\,(ml-nl-{{m}^{2}}+mn)=0\] Þ  \[{{n}^{2}}+{{l}^{2}}-2nl-4ml+4nl+4{{m}^{2}}-4mn=0\] Þ \[{{l}^{2}}+{{n}^{2}}+{{(2m)}^{2}}+2nl-4mn-4ml=0\] Þ \[{{(l+n-2m)}^{2}}=0\] Þ \[l+n=2m\] Þ l, m, n are in A.P.


You need to login to perform this action.
You will be redirected in 3 sec spinner