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

Explanation

To find the value of \( k \) in the polynomial \( x^2 + 2kx - 12 \) given that the sum of its zeroes is 1, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the coefficients of the polynomial**:
The polynomial is given as \( x^2 + 2kx - 12 \).
Here, we can identify:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 2k \) (coefficient of \( x \))
- \( c = -12 \) (constant term)

2. **Use the formula for the sum of the zeroes**:
The sum of the zeroes \( \alpha + \beta \) of a quadratic polynomial \( ax^2 + bx + c \) is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting the values of \( a \) and \( b \):
\[ \alpha + \beta = -\frac{2k}{1} = -2k \]

3. **Set the sum of the zeroes equal to 1**:
According to the problem, the sum of the zeroes is 1. Therefore, we can set up the equation:
\[ -2k = 1 \]

4. **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 \( -\frac{1}{2} \).

---