If one root of the quadratic equation `x^(2)-7x+k=0` is 2, find the value of k.

Answer

To find the value of \( k \) in the quadratic equation \( x^2 - 7x + k = 0 \) given that one of the roots is 2, we can follow these steps:

### Step 1: Substitute the root into the equation
Since we know that one root of the equation is 2, we can substitute \( x = 2 \) into the equation:

\[ 2^2 - 7(2) + k = 0 \]

### Step 2: Simplify the equation
Now, we will simplify the left side of the equation:

\[ 4 - 14 + k = 0 \]

### Step 3: Combine like terms
Combine the constants:

\[ -10 + k = 0 \]

### Step 4: Solve for \( k \)
To find \( k \), we can rearrange the equation:

\[ k = 10 \]

### Final Answer
Thus, the value of \( k \) is \( 10 \).

---