If the point (5,0), (0, -2) and (3, 6) lie on the graph of a polynomial. Then, which of the following is a zero of the polynomial?

Options

A. 5
B. 6
C. `-2`
D. not defined

Answer

To determine which of the given points corresponds to a zero of the polynomial, we need to understand the concept of zeros of a polynomial. A zero of a polynomial is a value of \( x \) for which the polynomial evaluates to zero (i.e., \( y = 0 \)).

Given the points:
1. \( (5, 0) \)
2. \( (0, -2) \)
3. \( (3, 6) \)

We will analyze each point to see if it represents a zero of the polynomial.

### Step 1: Identify the points
The points given are:
- \( (5, 0) \)
- \( (0, -2) \)
- \( (3, 6) \)

### Step 2: Check the y-values
To find the zeros, we need to check the y-values of each point:
- For the point \( (5, 0) \), the y-value is \( 0 \).
- For the point \( (0, -2) \), the y-value is \( -2 \).
- For the point \( (3, 6) \), the y-value is \( 6 \).

### Step 3: Determine which point has a y-value of zero
The only point where the y-value is zero is \( (5, 0) \). This means that when \( x = 5 \), the polynomial evaluates to zero.

### Conclusion
Thus, the zero of the polynomial is \( x = 5 \).

### Final Answer
The zero of the polynomial is \( 5 \).

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