2015-II-34

答案：B
由於 $\alpha$ 及 $\beta$ 為二次方程 $x^2 +kx-2=0$ 的兩根，則可得

$\begin{array}{rcl}
\alpha + \beta & = & -\dfrac{k}{1} \\
& = & -k \\
\alpha \beta & = & \dfrac{-2}{1} \\
& = & -2
\end{array}$

由此，可得

$\begin{array}{cl}
& \alpha^2 + \beta^2 \\
= & \alpha^2 +2\alpha \beta + \beta^2 – 2\alpha\beta \\
= & (\alpha + \beta)^2 – 2\alpha \beta \\
= & (-k)^2 -2(-2) \\
= & k^2 +4
\end{array}$