Correct Answer - Option 3 : -1
Calculation:
Let g(n) = n4 − n3 − n2 – 1 = 0 so we have a, b, c and d as the roots of g(n) so a4 − a3 − a2 – 1 = 0 etc.
f(n) = n2{n4 – n3 − n2 – 1 − (1/n)},
So, f(a) = a2(a4 − a3 − a2 − 1 – 1/a) = −a.
Hence, f(a) + f(b) + f(c) + f(d) = – (a + b + c + d) = –1.
If α , β, γ, δ are roots of a biquadratic equation ax4+ bx3 + cx2 + dx + e = 0, then
⇒ α + β + γ + δ = -b/a
⇒ αβ + βγ + γδ +αγ + αδ + βδ = c/a
⇒ αβγ + αγδ +αβδ + βγδ = -d/a
⇒ αβγδ = e/a