Answer:

-3

Step-by-step explanation:

[tex]x - 1 = 0 \\ x = 1[/tex]

[tex]4x {}^{3} + 3x {}^{3} - 4x + k = 0 \\ 4(1) { }^{3} + 3(1) {}^{3} - 4(1) + k = 0 \\ 4 + 3 - 4 + k = 0 \\ 3 + k = 0 \\ k = - 3[/tex]