Algebra

[Khushi Sharma]

Let P(x)=x3+ax2+b and Q(x)=x3+bx+a, where a, b are non-zero real numbers. Suppose that the roots of the equation P(x) = 0 are the reciprocals of the roots of the equation Q(x) = 0. Prove that a and b are integers. Find the greatest common divisor of P(2013! + 1) and Q(2013! + 1). (RMO 2013, Mumbai Region)

[Saumik Karfa]

This problem is already discussed here, we do not wish to write the same thing again.

Here is the direct link that contains the solution :https://www.meritnation.com/ask-answer/question/let-p-x-x3-ax2-b-and-q-x-x3-bx-a-where-a-b-are-non-zero-real/math/8608633

 

 

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