To solve the quadratic equation z² – 4z + 4 = 0, we can start by factoring the expression.
We look for two numbers that multiply to 4 (the constant term) and add up to -4 (the coefficient of z). The numbers that fit this requirement are -2 and -2. Thus, we can rewrite the equation as:
(z – 2)(z – 2) = 0
This can also be expressed as:
(z – 2)² = 0
Now, to find the value of z, we set the factor equal to zero:
z – 2 = 0
Solving for z, we get:
z = 2
Therefore, the possible value of z in the given quadratic equation is 2. This means that 2 is a repeated root, indicating that the parabola intersects the x-axis at a single point (2, 0), which confirms that it is a perfect square trinomial.