JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer If the product of roots of the equation\[{{x}^{2}}-3kx+2{{e}^{2\log k}}-1=0\]is 7, then its roots will real when [IIT 1984]

    A) \[k=1\]

    B) \[k=2\]

    C) \[k=3\]

    D)  None of these

    Correct Answer: B

    Solution :

    Given equation can be written as \[{{x}^{2}}-3kx+2{{k}^{2}}-1=0\] So the product of roots is  \[2{{k}^{2}}-1\]. But the product of roots is 7. Hence \[2{{k}^{2}}-1=7\Rightarrow 2{{k}^{2}}=8\Rightarrow k=\pm 2\]   But k cannot be negative.

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