[pdonis]

> the number of roots even for the same quadratic equation may depend on "private" thoughts such as whether complex roots are of interest

No. The number of roots that you care about might depend on your private thoughts; but the number of roots itself does not. It's a mathematical fact. It just might not be a mathematical fact that you actually care about. But what you care about is not part of math.

[lupire]

Why are you ignoring the quaternion roots? 3x3 matrix roots?

[pdonis]

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.