Problem 24

Algebra Level 5

\[\large (x_{1}-2x_{2}+x_{3})^2+(x_{2}-2x_{3}+x_{4})^2+(x_{2}-2x_{1})^2+(x_{3}-2x_{4})^2\]

Given that \(x_{1},x_{2},x_{3},x_{4}\) are the root of equation \(ax^4+bx^3+cx^2+dx+e=0\) also are real number satisfy \(\frac{1}{2}\leq x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}\leq 1\).

Let the sum of the minimum and maximum value is \(A\). Find \(\left \lceil A \right \rceil\).

This problem was in Vietnam TST a few year back.
This problem is in this Set.

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