10. Given that $a$ is a positive integer. If the roots of the equation $x^{3}+(a+17) x^{2}+(38-a) x-56=0$ are all integers, find the value of $a$ and the integer roots of the equation.
(Tip: The equation has an integer root $x=1$. When $x \neq$ 1, $x^{2}+(a+18) x+56=0$, its discriminant $\Delta=$ $(a+18)^{2}-224$ should be a perfect square, leading to $a=39$ or $a=12$. When $a=39$, the three roots of the original equation are $1,-1$ and -56; when $a=12$, the three roots of the original equation are $1,-2$ and -28.)