smc

An expression of the form $a{x}^2+bx+c$ has at least one real root when $b^2-4ac\ge 0$. Substituting $k$ for $b$ and $k^2$ for $c$, we have $$k^2-4k^2\ge 0$$ $$-3k^2\ge 0$$ but the range of $-3k^2$ is $(-\infty ,0]$, so the answer is $\boxed{\text{no values of }k}$