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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Mock Test - Complex Numbers and Quadratic Equations

  • question_answer
    If a, b\[\in \]R, \[a\ne 0\]and the quadratic equation \[a{{x}^{2}}-bx+1=0\]  has imaginary roots then \[(a+b+1)\]is

    A)  positive

    B)  negative

    C)  zero

    D)  dependent on the sign of b  

    Correct Answer: A

    Solution :

    [a] \[D={{b}^{2}}-4a<0\Rightarrow a>0\] Therefore the graph is concave upwards. \[f(x)>0,\forall x\in R\] \[\Rightarrow f(-1)>0\] \[\Rightarrow a+b+1>0\]


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