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JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer
    If the roots of the equation\[b{{x}^{2}}+cx+a=0\]be imaginary, then for all real values of\[x,\]the expression\[3{{b}^{2}}{{x}^{2}}+6bcx+2{{c}^{2}}\]is     AIEEE  Solved  Paper-2009

    A)  greater than 4ab

    B)        less than 4ab

    C)                        greater than -4ab            

    D) less than -4ab

    Correct Answer: C

    Solution :

    As,\[b{{x}^{2}}+cx+a=0\]has imaginary roots So,\[{{c}^{2}}<4ab\] Now,\[3{{b}^{2}}\text{ }{{x}^{2}}+6bcx+2{{c}^{2}}\] \[=3{{(bx+c)}^{2}}{{c}^{2}}\ge \text{ }{{c}^{2}}\ge 4ab\]


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