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

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