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

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