If `x=1` is a root of `x^(2)+kx+5=0`,

Options

A. `k= 5`
B. `k=6`
C. `k= -6`
D. none of these

Answer

To solve the problem, we need to determine the value of \( k \) given that \( x = 1 \) is a root of the quadratic equation \( x^2 + kx + 5 = 0 \).

### Step-by-Step Solution:

1. **Substitute the root into the equation**: Since \( x = 1 \) is a root, we can substitute \( x \) with \( 1 \) in the equation:
\[ 1^2 + k(1) + 5 = 0 \]

2. **Simplify the equation**: Calculate \( 1^2 \) which is \( 1 \):
\[ 1 + k + 5 = 0 \]

3. **Combine like terms**: Combine the constants \( 1 \) and \( 5 \):
\[ k + 6 = 0 \]

4. **Solve for \( k \)**: Isolate \( k \) by subtracting \( 6 \) from both sides:
\[ k = -6 \]

Thus, the value of \( k \) is \( -6 \).

### Final Answer:
The value of \( k \) is \( -6 \).