Problem 24

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

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 $\left \lceil A \right \rceil$ .

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This problem was in Vietnam TST a few year back.

This problem is in this Set .