For what real values of $k$, other than $k = 0$, does the equation $x^2 + kx + k^2 = 0$ have real roots?
$\textbf{(A)}\ {k  0} \qquad  \textbf{(C)}\ {k \ge 1} \qquad  \textbf{(D)}\ \text{all values of }{k}\qquad  \textbf{(E)}\ \text{no values of }{k}$
An expression of the form $ax^2+bx+c$ has at least one real root when $b^2-4ac \geq 0$.
Substituting $k$ for $b$ and $k^2$ for $c$, we have 
\[k^2-4k^2 \geq 0\]
\[-3k^2 \geq 0\]
but the range of $-3k^2$ is $(-\infty,0]$, so the answer is $\boxed{\text{(E)}}$