When the two quantics are the first derived functions of the same quantic of any odd order, the lineo-linear invariant does not vanish, but it is not an invariant of the single quantic.
Source: wiktionary
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74. The discriminant of a binary quantic, or the eliminant of a system of binary quantics, is an invariant. We can see a priori that this must be the case, for if a given quantic has a square factor, it will have a square factor still when it is linearly transformed; or if a system of quantics have a common factor, they will still have a common factor when the equations are transformed.
Source: wiktionary
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