Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0$ where $a > -1$. Then $\lim _{a \rightarrow 0^{+}} \alpha(a)$ and $\lim _{a \rightarrow 0^{+}} \beta(a)$ are
- A$-\frac{5}{2}$ and $1$
- B$-\frac{1}{2}$ and $-1$
- C$-\frac{7}{2}$ and $2$
- D$-\frac{9}{2}$ and $3$
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