# Limits, Limits, Limits, Limits

Algebra Level 3

$\left( \sqrt [ 3 ]{ 1+a } -1 \right) { x }^{ 2 }+\left( \sqrt { 1+a } -1 \right) x+(\sqrt [ 6 ]{ 1+a } -1)=0$

Let $$\alpha$$ and $$\beta$$ be the roots of the equation (of $$x$$) above for $$a> - 1$$.

Find the values of $$\displaystyle \lim_{a \to 0^+} \alpha$$ and $$\displaystyle \lim_{a \to 0^+} \beta$$ respectively.

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