The discriminant of `(x-2)^(2) =0` is positive.

Answer

To determine whether the statement "The discriminant of \((x-2)^2 = 0\) is positive" is true or false, we will first rewrite the equation in standard form and then calculate the discriminant.

### Step 1: Rewrite the equation
The given equation is \((x-2)^2 = 0\). We can expand this using the identity \((a-b)^2 = a^2 - 2ab + b^2\).

\[ (x-2)^2 = x^2 - 4x + 4 = 0 \]

### Step 2: Identify coefficients
From the standard form of the quadratic equation \(ax^2 + bx + c = 0\), we can identify the coefficients:
- \(a = 1\)
- \(b = -4\)
- \(c = 4\)

### Step 3: Calculate the discriminant
The discriminant \(D\) of a quadratic equation is given by the formula:

\[ D = b^2 - 4ac \]

Substituting the values of \(a\), \(b\), and \(c\):

\[ D = (-4)^2 - 4 \cdot 1 \cdot 4 \]
\[ D = 16 - 16 \]
\[ D = 0 \]

### Step 4: Analyze the result
Since the discriminant \(D\) is equal to 0, it indicates that the quadratic equation has two identical roots.

### Conclusion
The statement "The discriminant of \((x-2)^2 = 0\) is positive" is **false** because the discriminant is 0, not positive.

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