Normally "quadratic equation" means "over the complex numbers" (and the mention of "complex roots" in the post I responded to bears out that interpretation).
But yes, different mathematical models can give different answers for things like "number of roots of an equation". But that doesn't mean math depends on "private thoughts". It just means you need to specify which mathematical model you are talking about.
But yes, different mathematical models can give different answers for things like "number of roots of an equation". But that doesn't mean math depends on "private thoughts". It just means you need to specify which mathematical model you are talking about.