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11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer
    If \[a<0\] then the inequality \[a{{x}^{2}}-2x+4>0\] has the solution represented by [AMU 2001]

    A) \[\frac{1+\sqrt{1-4a}}{a}>x>\frac{1-\sqrt{1-4a}}{a}\]

    B) \[x<\frac{1-\sqrt{1-4a}}{a}\]

    C) x < 2

    D) \[2>x>\frac{1+\sqrt{1-4a}}{a}\]

    Correct Answer: A

    Solution :

    \[a{{x}^{2}}-2x+4>0\] Þ \[x=\frac{2\pm \sqrt{4-16a}}{2a}\] Þ \[x=\frac{1\pm \sqrt{1-4a}}{a}\]  \   \[\frac{1-\sqrt{1-4a}}{a}<x<\frac{1+\sqrt{1-4a}}{a}\].


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