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This is not a question; so I perfectly understand that it could be deleted almost immediately.

Yesterday, I was attending a New Year eve party and I was introduced to a young and brilliant lawyer. Hearing that I am (supposed to be) a mathematician, he seriously told me : "So, could you, by the end, explain to me why is $ax^2+bx+c$ always equal to $0$?".

I took it as a very good joke. The problem is that this was not a joke at all : the guy was serious !!

I am not an educator but I think that there are a lot of questions coming out from it.

I would really appreciate your opinions.

Since questions are required :

what can we do to make better understanding of mathematics starting with young people ?

how can we make mathematics more attractive ?

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    $\begingroup$ @JW. I really don't think what to ask as a question (could you help me to formulate one ?). I discovered again how poorly can be explained things by bad educators (I suffered many of them myself). Nobody ever told me that mathematics includes beauty and fun plus many other pleasant things I learned with age. $\endgroup$ – Claude Leibovici Jan 1 '16 at 15:55
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    $\begingroup$ You got proposals for some questions. If you want to ask one of them please edit the post to include it. I am afraid we cannot keep this post open "as is." As you know SE is for questions (and answers) not open ended discussions. $\endgroup$ – quid Jan 1 '16 at 16:56
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    $\begingroup$ Thanks for the effort, but I am sorry. These questions you added are much too broad and seem unrelated to the example you gave. $\endgroup$ – quid Jan 1 '16 at 17:09
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    $\begingroup$ I like the spirit of this. I agree things are too broad though. I believe that most students are interested in maths initially but are later switched off. $\endgroup$ – Karl Jan 1 '16 at 20:29
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    $\begingroup$ @JoelReyesNoche. May be, I did not explain properly : the guy was wondering why $ax^2+bx+c$ is always equal to $0$. $\endgroup$ – Claude Leibovici Jan 2 '16 at 13:18