If `1/2` is a root of the equation `x^2+kx-5/4=0,` then find the value of k.

Options

A. `2`
B. `-2`
C. `1/4`
D. `1/2`

Explanation

To find the value of \( k \) in the equation \( x^2 + kx - \frac{5}{4} = 0 \) given that \( \frac{1}{2} \) is a root, we will substitute \( x = \frac{1}{2} \) into the equation and solve for \( k \).

### Step-by-Step Solution:

1. **Substitute the root into the equation**:
\[ \left(\frac{1}{2}\right)^2 + k\left(\frac{1}{2}\right) - \frac{5}{4} = 0 \]

2. **Calculate \( \left(\frac{1}{2}\right)^2 \)**:
\[ \frac{1}{4} + \frac{k}{2} - \frac{5}{4} = 0 \]

3. **Combine like terms**:
To combine the fractions, we can rewrite \( \frac{5}{4} \) as \( \frac{5}{4} \):
\[ \frac{1}{4} - \frac{5}{4} + \frac{k}{2} = 0 \]
This simplifies to:
\[ -\frac{4}{4} + \frac{k}{2} = 0 \]
or
\[ -1 + \frac{k}{2} = 0 \]

4. **Isolate \( k \)**:
Add 1 to both sides:
\[ \frac{k}{2} = 1 \]
Now, multiply both sides by 2:
\[ k = 2 \]

### Final Answer:
The value of \( k \) is \( 2 \).