jmc

Recall that for an equation of the form $a{x}^2+bx+c=0$, the sum of roots is equal to $-b/a$ and the product of the roots is equal to $c/a$.

So, we can write the set of equations $$\begin{array}{rl}3-\frac{4}{3}& =\frac{5}{k}\\ -4& =\frac{-12}{k}\end{array}$$

The second equation tells us immediately that $k=\boxed{3}$.