<s>[INST] Find the quadratic equation equation of $x_1, x_2$. 
Let $x_1 = 1 + \sqrt 3, x_2 = 1-\sqrt 3$. Find the quadratic equation $ax^2+bx+c = 0$ which $x_1, x_2$ are it's solutions.  

By Vieta's theorem:  
$$x_1\cdot x_2 = \frac{c}{a} \implies c=-2a$$
$$x_1 + x_2 = -\frac{b}{a} \implies b = -2a$$
Therefore, $b=c$
So we have a quadratic equation with the form:
$$-\frac{b}{2}x^2 + bx + b = 0$$
Applying $x_1$ for our equation I get $b=0$. Why? 
The final answer is: $x^2-2x-2$.
 [/INST] Is $x_1$ and $x_2$ are the solution than you can write
$$(x_1-x)(x_2-x)=0$$
which is
$$x^2-(x_1+x_2)\cdot x+x_1x_2=0$$
Thus $a=1$, $b=-x_1-x_2$ and $c=x_1x_2$
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