This question comes from projective geometry. A degenerate conic $C$ is defined as $$C=lm^T+ml^T,$$
where $l$ and $m$ are different lines. It can be easily shown, that all points on $l$ and m lie on the $C$. Because, for example, if $x\in l$, then by definition $l^Tx=0$ and plugging it into conic equation makes it true.
Question: Find the rank of $C$.
(We can limit ourself to 3-dimensional projective space.)
P.S. I'm reading a book, where it is guessed and checked, but I would like to have a proof without guessing. I do not provide the guess, since it can distract you, but if you really need it just leave a note.