To determine the possible value or values of [tex]\( z \)[/tex] for the quadratic equation [tex]\( z^2 - 4z + 4 \neq 0 \)[/tex], let's first examine the equation more closely.
We start with the given quadratic equation:
[tex]\[ z^2 - 4z + 4 \neq 0 \][/tex]
To solve this, let's factor the quadratic expression on the left-hand side:
[tex]\[ z^2 - 4z + 4 = (z - 2)^2 \][/tex]
Therefore, we can rewrite the inequality as:
[tex]\[ (z - 2)^2 \neq 0 \][/tex]
A perfect square like [tex]\((z - 2)^2\)[/tex] equals zero when [tex]\( z = 2 \)[/tex]. However, in the given inequality, we seek values of [tex]\( z \)[/tex] that do not make the equation zero. Therefore, for [tex]\( (z - 2)^2 \neq 0 \)[/tex], [tex]\( z \)[/tex] must not be equal to 2.
In other words:
[tex]\[
z \neq 2
\][/tex]
After determining that [tex]\( z \neq 2 \)[/tex], we need to select the appropriate answer from the provided choices. The only value that fits our condition precisely is:
B. [tex]\( z = 2 \)[/tex]
C. [tex]\( z \neq 2 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
