# 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.

###### This is a modified AIME problem.

Also try this.