JEE Advanced 2014 Mathematics question

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation

p(p(x)) = 0

has

Answer: (D)

Solution

Purely imaginary roots ±ik (k > 0) with real coefficients mean . Then p(p(x)) = 0 requires , i.e. . The right side has non-zero real and

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Question ID VK-026353