JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Relation between roots and coefficients

  • question_answer
    If the roots of the equation \[a{{x}^{2}}+bx+c=0\] are reciprocal to each other, then [RPET 1985]

    A) \[a-c=0\]

    B) \[b-c=0\]

    C) \[a+c=0\]

    D) \[b+c=0\]

    Correct Answer: A

    Solution :

    Given equation is \[a{{x}^{2}}+bx+c=0\]and whose roots are \[\alpha \]and \[\frac{1}{\alpha }\], then the product of roots is \[\alpha .\frac{1}{\alpha }=\frac{c}{a}\Rightarrow c=a\Rightarrow a-c=0\]


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