# Archit's Challenge 7

Algebra Level 5

For real numbers $$a,b,c,d,p,q,r,s$$ with $$b-d\geq 5$$, let the roots of the quartic polynomial $$f(x) = x^4 + ax^3 + bx^2 + cx + d$$ be $$p,q,r$$ and $$s$$. Find the minimum value of

$(1+p^2)(1+q^2)(1+r^2)(1+s^2).$

×