Problem (Algebra):
Let $T$ = 2069, and let $K$ be the sum of the digits of $T$. Let $r$ and $s$ be the two roots of the polynomial $x^{2}-18 x+K$. Compute $|r-s|$.

Solution:
Note that $|r-s|=\sqrt{r^{2}-2 r s+s^{2}}=\sqrt{(r+s)^{2}-4 r s}$. By Vieta's Formulas, $r+s=-(-18)$ and $r s=K$, so $|r-s|=\sqrt{18^{2}-4 K}$. With $T=2069, K=17$, and the answer is $\sqrt{324-68}=\sqrt{256}=16$.

Final answer: 16