All you need is a 4d imagination

Algebra Level 4

The range of values of $k$ such that the only solution to

$a^2 + kab + b^2 = 0$

is the trivial solution $a=b=0$ , is $k \in (m,n)$ .

Find the value of $m^2+n^2$ ?

The title refers to the graph of $w=f(x,y,z)=x^2+xyz+z^2$ ; if you can imagine that graph then the answer should come naturally. This has no relevance whatsoever to the answer.