Why use OR instead of AND for x-intercepts in y=(x-2)(x-3)

[TyErd]

Alright let's says for example we were to sketch y=(x-2)(x-3). You would find x intercepts and you would write it as x-2=0 OR x-3=0, thus x=2 OR x=3. Why do we use the word OR when we use both of the intercepts to sketch the graph anyway? Why cannot we use AND instead.

 

[Mentallic]

To find the x-intercepts, which is where y=0, when you have two variables multiplied together to equal zero, you only need one or the other to be 0.

e.g. if you have ab=0, where a and b are not equal, then a can be 0 or b can be 0, but since a is not equal to b then you can't have a and b are 0.

Same thing goes with that quadratic. (x-2)(x-3)=0 means that for some value x, the first factor (x-2) will equal zero while the second won't, and similarly for the second factor. This is why it is said x-2=0 OR x-3=0.