# What happens if we forget a trivial assumption ?

Last week, @dmonniaux published an interesting post entitled l’erreur n’a rien d’original  on  his blog. He was asking the following question : let $a$, $b$ and $c$ denote three real-valued coefficients, under which assumption on those three coefficients does $ax^2+bx+c$ has a real-valued root ?

Everyone aswered $b^2-4ac\geq 0$, but no one mentioned that it is necessary to have a proper quadratic equation, first. For instance, if both $a$ and $b$ are null, there are no roots.