# Everybody loves to root for a nuisance!!

Algebra Level 4

Let $$a$$, $$b$$, $$c$$, $$d$$ be real numbers and all zeroes $$\beta_1, \beta_2, \beta_3,$$ and $$\beta_4$$ of the polynomial $$P(x)=x^4+ax^3+bx^2+cx+d$$ are real. Find the smallest value the product $$(\beta_1^2+1)(\beta_2^2+1)(\beta_3^2+1)(\beta_4^2+1)$$ can take.

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