If the sum of zeroes of the polynomial `x^(2)+2kx-12` is 1, find the value of k.

Explanation

To solve the problem, we need to find the value of \( k \) given that the sum of the zeroes of the polynomial \( x^2 + 2kx - 12 \) is equal to 1.

### Step-by-Step Solution:

1. **Identify the Polynomial**: The given polynomial is \( x^2 + 2kx - 12 \).

2. **Understand the Sum of Zeroes**: Let the zeroes of the polynomial be \( \alpha \) and \( \beta \). According to the problem, we know that:
\[ \alpha + \beta = 1 \]

3. **Use the Relationship for Sum of Zeroes**: For a quadratic polynomial of the form \( ax^2 + bx + c \), the sum of the zeroes is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Here, \( a = 1 \) (coefficient of \( x^2 \)) and \( b = 2k \) (coefficient of \( x \)).

4. **Substituting Values**: Plugging in the values of \( a \) and \( b \) into the formula gives:
\[ \alpha + \beta = -\frac{2k}{1} = -2k \]

5. **Set the Two Expressions Equal**: Since we know that \( \alpha + \beta = 1 \), we can set the two expressions equal to each other:
\[ -2k = 1 \]

6. **Solve for \( k \)**: To find \( k \), we can rearrange the equation:
\[ 2k = -1 \]
Dividing both sides by 2 gives:
\[ k = -\frac{1}{2} \]

### Final Answer:
The value of \( k \) is \( -\frac{1}{2} \).