6.125. Find the coefficients $A$ and $B$ of the equation $x^{2}+A x+B=0$, if it is known that the numbers $A$ and $B$ are its roots.
## Solution.

By Vieta's theorem

$$
\left\{\begin{array} { l } 
{ A + B = - A , } \\
{ A B = B }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ 2 A + B = 0 , } \\
{ B ( A - 1 ) = 0 }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ A _ { 1 } = 0 , } \\
{ B _ { 1 } = 0 }
\end{array} \text { or } \left\{\begin{array}{l}
A_{2}=1, \\
B_{2}=-2
\end{array}\right.\right.\right.\right.
$$

Answer: $A_{1}=B_{1}=0 ; A_{2}=1, B_{2}=-2$.