Zero to equations and inequalities

[elmestlol]

Hello my question is why do we set some equations and inequalities to 0, for example quadratic equations/inequalities. I know that they should be 0, but why. How did people come with this when they invented it.

 

[Goongyae]

Are you asking why
x^2=5x+6

will often be rewritten as
x^2-5x-6 = 0
?

The only reason is that it is familiar. There is no difference in the information content of these equivalent equations.

 

[uart]

elmestlol, are you familiar with the method of solving simple quadratic equations using factorization?

Think carefully about why an RHS of zero is particularly useful for solving an equation in factorized form.

 

[uart]

elmestlol, are you familiar with the method of solving simple quadratic equations using factorization?

Think carefully about why an RHS of zero is particularly useful for solving an equation in factorized form.

 

[elmestlol]

Yes I know it . Ok maybe I understand now why is it used.

 

[Mentallic]

I actually find the idea of factorizing quadratics that are set to zero very smart indeed. You can explain to anyone that if you multiply two numbers together and they equal zero, then either one or the other or both have to be zero. They reply with "well duh, obviously" but all of a sudden it becomes much less intuitive at first glance when solving quadratics.

 

[HallsofIvy]

it is the "zero property" of multiplication: If AB= 0 then either A= 0 or B= 0 or both.

But if AB= C where C is not 0, we know nothing about A and B separately.