Question

If 2 is one root of the equation 4x3 + kx - 24 = 0, then the value of k is

Answer 1

Answer:

B

Step-by-step explanation:

We are given the equation:

$\displaystyle 4x^3 + kx - 24 = 0$

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:

$\displaystyle 4(2)^3 + k(2) - 24 = 0$

Solve for k:

$\displaystyle \begin{aligned} 4(2)^3 + k(2) - 24 & = 0 \\ \\ 32 + 2k - 24 & = 0 \\ \\ 2k + 8 & = 0 \\ \\ k & = - 4\end{aligned}$

Hence, the value of k is -4.

In conclusion, our answer is B.