Let y=f(x) be a polynomial function whose degree is greater than zero such that f(α) and f(1α) satisfy the equation x3−(1−a)x2−2ax+a=0 ∀ α∈R−{0} where a∈R. If d4ydx4∣∣∣x=2=0 and d3ydx3∣∣∣x=2=−6, then for α=2, the value of 8a is

Let y=f(x) be a polynomial function whose degree is greater than zero

1.	Let y=f(x) be a polynomial function whose degree is greater than zero such that f(α) and f(1α) satisfy the equation x3−(1−a)x2−2ax+a=0 ∀ α∈R−{0} where a∈R. If d4ydx4∣∣∣x=2=0 and d3ydx3∣∣∣x=2=−6, then for α=2, the value of 8a is
Answer» Let $y = f (x)$ be a polynomial function whose degree is greater than zero such that $f (α)$ and $f (\frac{1}{α})$ satisfy the equation $x^{3} - (1 - a) x^{2} - 2 a x + a = 0$ $\forall α \in R - {0}$ where $a \in R$ . If ${\begin{matrix} \frac{d^{4} y}{d x^{4}} \end{matrix} ∣ ∣ ∣}_{x = 2} = 0$ and ${\begin{matrix} \frac{d^{3} y}{d x^{3}} \end{matrix} ∣ ∣ ∣}_{x = 2} = - 6,$ then for $α = 2,$ the value of $8 a$ is