I am confused on the notation used when writing down the solution of x and y in quadratic equations. For example in $$x^2+2x-15=0$$, do I write :

$$x=-5$$ AND $$x=3$$

or is it

$$x=-5$$ OR $$x=3$$

which is it and why? I thought that because x can only equal one of the values when you substitute it in so it would be OR, however there are sometimes 2 roots of a quadratic so is it more correct to use AND? What about for the value of $$y$$, is it the same?

It depends on the context. Consider these two examples:

• The solutions to $$x^2+2x-15=0$$ are $$x=-5$$ and $$x=3$$.

• If $$x^2+2x-15=0$$ then $$x=-5$$ or $$x=3$$.

In both cases, it would be wrong to use 'or' in stead of 'and' or 'and' in stead of 'or'.

• okay. So it depends on the wording of the question?
– yt.
Feb 9, 2019 at 21:40
• Also does this apply for the solutions to $y$ as well?
– yt.
Feb 9, 2019 at 22:11

Firstly, it's impossible that $$x=-5$$ and $$x=3$$.

We need to solve $$(x+5)(x-3)=0,$$ which gives $$x+5=0$$ or $$x-3=0$$ and from here we get a right answer.

Actually, to solve an equation with one variable it says to find a full set of the roots.

You can say that $$-5$$ and $$3$$ they are roots of the equation and we see that our equation has no another roots.

• All of it's true, but that's contrived. How do you come from logical conjunction to multiplication? If you want to show that both $x=-5$ and $x=3$ can't be true, then show it directly. This way it's rather non-obvious (given that the question is relatively simple). Feb 9, 2019 at 21:05
• @enedil This is a way to understand why we need to say $x=-5$ or $x=3$. I added something for you. Feb 9, 2019 at 21:12