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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?

Thanks in advance

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2 Answers 2

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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'.

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

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  • $\begingroup$ 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). $\endgroup$
    – enedil
    Feb 9, 2019 at 21:05
  • $\begingroup$ @enedil This is a way to understand why we need to say $x=-5$ or $x=3$. I added something for you. $\endgroup$
    – Michael Rozenberg
    Feb 9, 2019 at 21:12

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