Find a number k such that 4 and 1 are the solutions
of x^2 - 5x + k = 0.
It sure is! And I will confess that I would have suggested either
1) Use the quadratic formula: $\displaystyle x= \frac{5\pm\sqrt{25- 4k}}{2}$
and set $\displaystyle \frac{5+ \sqrt{25- 4k}}{2}= 4$ and $\displaystyle \frac{5- \sqrt{25- 4k}}{2}= 1$ and solve for k
or
2) Write $\displaystyle x^2- 5x+ k= (x- 1)(x- 4)$, multiply it out and solve for k.
But skeeter's suggestion is far simpler than either of those.