Given:
p(x) = 6x3 + 3x2 – 5x + 1
= 6x3 – (–3) x2 + (–5) x – 1
Comparing the polynomial with x3 – x2 (α + β + γ) + x (αβ + βγ + γα) – αβγ,
we get:
αβ + βγ + γα = –5
and αβγ = – 1
∴ \((\frac{1}{\alpha}+\frac1{\beta}+\frac1{\gamma})\)
= \((\frac{\beta\gamma+\alpha\gamma+\alpha\beta}{\alpha\beta\gamma})\)
= \((\frac{-5}{-1})\)
= 5