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 https://latex.codecogs.com/gif.latex?a, https://latex.codecogs.com/gif.latex?b and https://latex.codecogs.com/gif.latex?c denote three real-valued coefficients, under which assumption on those three coefficients does https://latex.codecogs.com/gif.latex?ax^2+bx+c has a real-valued root ?

Everyone aswered https://latex.codecogs.com/gif.latex?b^2-4ac\geq%200, but no one mentioned that it is necessary to have a proper quadratic equation, first. For instance, if both https://latex.codecogs.com/gif.latex?a and https://latex.codecogs.com/gif.latex?b are null, there are no roots.

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