6.344 Find the coefficients $a$ and $b$ of the equation $x^{4}+x^{3}-18 x^{2}+a x+b=0$, if among its roots there are three equal integer roots.
Solution. Let $x_{1}=x_{2}=x_{3}, x_{4}$ be the roots of the original equation. By Vieta's theorem,

we have: $\left\{\begin{array}{l}3 x_{1}+x_{4}=-1, \\ 3 x_{1}^{2}+3 x_{1} x_{4}=-18, \\ x_{1}^{3}+3 x_{1}^{2} x_{4}=-a, \\ x_{1}^{3} x_{4}=b\end{array} \Rightarrow x_{1}^{2}+x_{1}\left(-1-3 x_{1}\right)=-6 \Rightarrow x_{1}=-2 \Rightarrow\right.$

$\Rightarrow x_{4}=5 \Rightarrow a=-52, b=-40$.

Answer: $a=-52, b=-40$.