The equations $x^2-5x+6=0$ and $x^2-kx+8=0$ have a common root, and $k$ is an integer. Find $k$.

The roots of the first are 2 and 3. Root 2: 4 − 2k + 8 = 0 gives k = 6. Root 3 would give k = 17/3, not an integer. So k = 6.