To determine which function has the same zeros as [tex]\( f(x) = x^3 - 2x^2 - 24x \)[/tex], we need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
The zeros of the function [tex]\( f(x) \)[/tex] are the solutions to the equation:
[tex]\[ x^3 - 2x^2 - 24x = 0 \][/tex]
Upon solving this equation, we find the zeros to be [tex]\( x = -4 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 6 \)[/tex].
Now, let's analyze the options to determine which function has the same zeros.
Without the actual function choices (A, B, and C) provided, it's impossible to match them directly. However, the correct function will have the same zeros [tex]\( x = -4 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 6 \)[/tex].
For instance, if you see another polynomial in factored form such as:
[tex]\[ g(x) = k(x + 4)(x)(x - 6) \][/tex]
where [tex]\( k \)[/tex] is any constant, it will have the same zeros as [tex]\( f(x) \)[/tex].
Thus, to determine the correct function, you need to select the one that yields the same zeros of [tex]\( -4 \)[/tex], [tex]\( 0 \)[/tex], and [tex]\( 6 \)[/tex]. Analyze the provided options and choose accordingly.
