To determine at which values of [tex]\( x \)[/tex] the function [tex]\( f(x) = x^2 - 4x \)[/tex] equals zero, let's solve the equation [tex]\( x^2 - 4x = 0 \)[/tex].
First, we factor the equation:
[tex]\[ x^2 - 4x = 0 \][/tex]
[tex]\[ x(x - 4) = 0 \][/tex]
The solutions to this equation are given by setting each factor equal to zero:
1. [tex]\( x = 0 \)[/tex]
2. [tex]\( x - 4 = 0 \)[/tex]
Solving [tex]\( x - 4 = 0 \)[/tex], we get:
[tex]\[ x = 4 \][/tex]
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex] are:
[tex]\[ x = 0 \text{ and } x = 4 \][/tex]
Thus, the function [tex]\( f(x) = x^2 - 4x \)[/tex] is zero at [tex]\( x = 0 \)[/tex] and [tex]\( x = 4 \)[/tex].
