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 Condition for common roots, Quadratic expressions and Position of roots

  • question_answer
    If \[a{{x}^{2}}+bx+c=0\] and \[b{{x}^{2}}+cx+a=0\] have a common root \[a\ne 0\], then \[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}=\] [IIT 1982; Kurukshetra CEE 1983]

    A) 1

    B) 2

    C) 3

    D) None of these

    Correct Answer: C

    Solution :

    The condition for common roots gives \[{{(bc-{{a}^{2}})}^{2}}=(ca-{{b}^{2}})(ab-{{c}^{2}})\] On simplification gives \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\]


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