The equations x² - 5x + 6 = 0 and x² + kx - 12 = 0 share x=3 as a common root. What is the value of k?

The first equation factors as $(x-2)(x-3) = 0$, confirming that 3 is a root. Since $x = 3$ is also a root of $x^2 + kx - 12 = 0$, substitute: $9 + 3k - 12 = 0$, so $3k = 3$ and $k = 1$, choice C. Check: $x^2 + x - 12 = (x+4)(x-3)$, which has root 3. Choice A (4) is the other root's size (the second root is $-4$) and not $k$. Choice B ($-1$) has the wrong sign. Choice D ($-4$) is the other root of the second equation. The question asks for the coefficient $k$, not for a root.