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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
    If \[a+b+c=0,\]\[a\ne 0,a,b,c\in Q\], then both the roots of the equation \[a{{x}^{2}}+bx+c=0\] are

    A) Rational

    B) Non-real

    C) Irrational

    D) Zero

    Correct Answer: A

    Solution :

    \[D\equiv {{b}^{2}}-4ac={{(-a-c)}^{2}}-4ac\]  \[(\because a+b+c=0)\]     \[={{(a+c)}^{2}}-4ac={{(a-c)}^{2}}\ge 0\] Hence roots are rational.


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