If $α$ and $β$ be the roots of ax2 + bx + c = 0 then $\underset{x→α}{\lim}(1+ax^2+bx+c)^{1/(x-a)}$ is :

$a(α-β)$ $ln|a(α-β)|$ $e^{(α-β)}$ $e^{a(α-β)}$

$e^{a(α-β)}$

$ax^2+ bx + c = 0, α, β$ are the roots   $⇒ax^2+bx+c≡a(x-α)(x-β)$ $\underset{x→α}{\lim}(1+a(x-α)(x-β))\frac{1}{x-α}$ $=\underset{(x→α)→0}{\lim}[1+a(x-α)(x-β)]\frac{a(x-β)}{a(x-β)(x-α)}=\underset{x→α}{\lim}e^{a(x-β)}=e^{a(α-β)}$