p: x = 5 or x = 1 is the root of equation `(x - 5)^2 `= 0, statement p is true since

Options

A. Both the component statements are false
B. Both the component statements are true
C. One of the component statements is true
D. None of these

Answer

To solve the question, we need to analyze the statement \( p: x = 5 \) or \( x = 1 \) is the root of the equation \( (x - 5)^2 = 0 \).

### Step-by-Step Solution:

1. **Understand the Equation**: We start with the equation \( (x - 5)^2 = 0 \). This is a quadratic equation in the form of a perfect square.

2. **Set the Equation to Zero**: To find the roots, we can take the square root of both sides. So, we have:
\[ (x - 5) = 0 \]

3. **Solve for x**: Now, we solve the equation:
\[ x - 5 = 0 \implies x = 5 \]

4. **Identify the Roots**: The only root of the equation \( (x - 5)^2 = 0 \) is \( x = 5 \).

5. **Evaluate the Statement p**: The statement \( p \) claims that \( x = 5 \) or \( x = 1 \) is a root of the equation. Since we found that the only root is \( x = 5 \), we can conclude that the part of the statement claiming \( x = 1 \) is false.

6. **Conclude the Truth of Statement p**: Since at least one part of the statement \( p \) (specifically \( x = 5 \)) is true, we can conclude that statement \( p \) is true.

7. **Select the Correct Option**: Based on the analysis, the correct option is that one of the component statements is true, which corresponds to option C.

### Final Answer:
The statement \( p \) is true since \( x = 5 \) is the only root of the equation \( (x - 5)^2 = 0 \).

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