Answer:
B
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle 4x^3 + kx - 24 = 0[/tex]
And that x = 2 is a root. And we want to determine the value of k.
By definition, since x = 2 is a root of the equation, when x = 2, the equation must equal zero:
[tex]\displaystyle 4(2)^3 + k(2) - 24 = 0[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} 4(2)^3 + k(2) - 24 & = 0 \\ \\ 32 + 2k - 24 & = 0 \\ \\ 2k + 8 & = 0 \\ \\ k & = - 4\end{aligned}[/tex]
Hence, the value of k is -4.
In conclusion, our answer is B.
