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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 \[a+b+c=0\], then the roots of the equation \[4a{{x}^{2}}+3bx+2c=0\] are

    A) Equal

    B) Imaginary

    C) Real

    D) None of these

    Correct Answer: C

    Solution :

    We have \[4a{{x}^{2}}+3bx+2c=0\] Let roots are \[\alpha \] and  \[\beta \] Let  \[D={{B}^{2}}-4AC\]\[=\,\,9{{b}^{2}}-4(4a)(2c)=9{{b}^{2}}-32ac\] Given that, \[(a+b+c)=0\Rightarrow b=-(a+c)\] Putting this value, we get \[=9{{(a+c)}^{2}}-32ac=9{{(a-c)}^{2}}+4ac\]. Hence roots are real.


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