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Equation:

$x^2-x-6=0$

The two roots of this equation are $3$ and $-2$. When writing the answer can I also write it as $-2, 3$ or do I have to maintain a certain order?

Rick
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Russell
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    Ordering elements of a set doesn't matter. – hamam_Abdallah Jun 06 '20 at 13:16
  • Saying it either way, if you mean the set of zeroes of the equation, then it makes no difference. – coffeemath Jun 06 '20 at 13:16
  • @hamam_Abdallah I was answering a multiple answer question which asked to determine the roots of the equation. One of the options was 3, -2 and one of the other option was -2, 3. Please note that the options didn't have any opening or closing second bracket {}. Does this make any difference, or is it a problem with the question? – Russell Jun 06 '20 at 13:22
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    ${a,b,c}={a,c,b}={b,c,a}=...} – hamam_Abdallah Jun 06 '20 at 13:24
  • @hamam_Abdallah I understand your first comment. What I wanted to know is do we always write the roots of the equation as elements of a set? can we write the roots in a way where the order is matter? – Russell Jun 06 '20 at 13:27
  • The order of the roots makes no difference. In fact, I can hardly believe what you say about the multiple-choice question. Are you sure the second one wasn't ${2,-3}$? – TonyK Jun 06 '20 at 13:50
  • @TonyK I'm sure. There are four options in total. A. {2, 3} B. {-3, -2} C. {3, -2} D. {-2, 3}. It could be a printing mistake, but there's no way to know. – Russell Jun 06 '20 at 14:52

2 Answers2

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The order of the roots should not matter, the solutions {-2,3} still conveys the same meaning as {3, -2}. Edit: some people may prefer you to order your solution from the least greatest to greatest value for ease of marking (e.g. -2 then 3), but mathematically, it makes no difference.

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If the question offers the two choices you gave us in a comment, $-2, 3$ and $3, -2$, then the question is wrong. Either answer is correct. Perhaps one of the suggested answers should have had the signs the other way $2, -3$ ( not the order the other way). Then they might be looking for a particular error you might have made.

Ethan Bolker
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