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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
    The condition for the roots of the equation,\[({{c}^{2}}-ab){{x}^{2}}-\]\[2({{a}^{2}}-bc)x+({{b}^{2}}-ac)=0\] to be equal is   [TS Rajendra 1982]

    A) \[a=0\]

    B) \[b=0\]

    C) \[c=0\]

    D) None of these

    Correct Answer: A

    Solution :

    According to question, \[4{{({{a}^{2}}-bc)}^{2}}-4({{c}^{2}}-ab)({{b}^{2}}-ac)=0\] Þ \[a({{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc)=0\] Þ \[a=0\]or \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\]


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