# USAMO Problem 1

Algebra Level 5

Let $$a$$, $$b$$, $$c$$, $$d$$ be real numbers such that $$b-d \ge 5$$ and all zeros $$x_1, x_2, x_3,$$ and $$x_4$$ of the polynomial $$P(x)=x^4+ax^3+bx^2+cx+d$$ are real. Find the smallest value the product $$(x_1^2+1)(x_2^2+1)(x_3^2+1)(x_4^2+1)$$ can take.This problem is part of this set.

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