# How to enumerate the solutions of a quadratic equation

When we solve a quadratic equation, and let's assume that the solutions are $x=2$, $x=3$, should I say

1. $x=2$ and $x=3$
2. $x=2$ or $x=3$.

What is the correct way to say it?

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The answer "The solutions are $x=2$ and $x=3$" is perfectly fine, sounds a little better than "or." If we leave out "the solutions are" then I would say the balance tilts to or. –  André Nicolas May 2 '13 at 17:03
The second way is better. $x$ can't be both $2$ and $3$ at the same time. –  Stefan Smith May 2 '13 at 23:48

Since $x$ cannot simultaneously equal both $2$ and $3$, you need to use $x = 2$ or $x = 3$.

You can say that both $x = 2$ and $x = 3$ are solutions to the equation, but that simply means that when $x = 2$, the equation is satisfied, and when $x = 3$, the equation is satisfied. But clearly, when $x = 2, x\neq 3$ and when $x = 3, x \neq 2$. I.e. it makes no sense to say $x = 2 = 3$, e.g. solves the equation.

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Always clean +1 –  Amzoti May 3 '13 at 0:22

It depends on how you write the solution.

$(x-2)(x-3)=0$, so $x=2$ or $x=3$.

$(x-2)(x-3)=0$, so the solutions are $x=2$ and $x=3$.

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Are you the same as this person? math.stackexchange.com/users/43115/jasper-loy –  user17762 May 2 '13 at 17:06
Why? You mean user17762? –  Reader May 2 '13 at 17:13
Oh No I am not Jasper loy. Absolutely not –  Reader May 2 '13 at 17:14

You should say $$x=2 \color{red}{\textbf{ or }}x=3.$$ $x=2$ and $x=3$ is wrong since $x$ cannot be equal to $2$ and $3$ simultaneously, since $2 \neq 3$.

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