Let f(x) be a polynomial satisfying limx→∞ x2f(x)2x5+3=6 and f(1)=3,f(3)=7 and f(5)=11 Then the value of |f(0)| is _______ .

Since limx→∞ x2f(x)2x5+3=6 which is finite and non-zero, f(x) must be polynomial of degree '3'.Also f(1) = 3, f(3) = 7 and f(5) = 11∴ f(x)=λ(x−1)(x−3)(x−5)+(2x+1)⇒limx→∞ x2(λ(x−1)(x−3)(x−5)+2x+1)2x5+3=6⇒ λ2=6⇒λ=12∴   f(x)=12(x−1)(x−3)(x−5)+(2x+1)So, f(0) = 12(-1)(-3)(-5)+1= 179