Official solution
81x2 + kx + 256 = 0 ; x = \[\alpha \], \[\alpha \]3
\[ \Rightarrow \] \[\alpha \]4 = \[{{256} \over {81}}\] \[ \Rightarrow \] \[\alpha \] = \[ \pm \] \[{{4} \over {3}}\]
Now - \[{k \over {81}}\] = \[\alpha \] + \[\alpha \]3 = \[ \pm \] \[{{100} \over {27}}\]
\[ \Rightarrow \] k = \[ \pm \]300