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INMO 2003 Problem 3

  • Answer

Show that for every real number aa the equation

8x4−16x3+16x2−8x+a=08 x^{4}-16 x^{3}+16 x^{2}-8 x+a=0

has at least one non-real root and find the sum of all the non-real roots of the equation.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

1 \text{ for } a \leq \frac{3}{2}, \text{ and } 2 \text{ for } a > \frac{3}{2}

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