One of the roots of the equation `x^(2)-12x+k=0` is `x=3`. The value of k is :

Options

A. `k=-27
B. `k=27
C. `k=4`
D. `k=-9`

Answer

To find the value of \( k \) in the quadratic equation \( x^2 - 12x + k = 0 \) given that one of the roots is \( x = 3 \), we can follow these steps:

### Step 1: Substitute the root into the equation
Since \( x = 3 \) is a root of the equation, we can substitute \( x \) with \( 3 \) in the equation:

\[ 3^2 - 12 \cdot 3 + k = 0 \]

### Step 2: Calculate \( 3^2 \)
Calculating \( 3^2 \):

\[ 3^2 = 9 \]

### Step 3: Calculate \( -12 \cdot 3 \)
Now, calculate \( -12 \cdot 3 \):

\[ -12 \cdot 3 = -36 \]

### Step 4: Substitute the values back into the equation
Now substitute these values back into the equation:

\[ 9 - 36 + k = 0 \]

### Step 5: Simplify the equation
Now, simplify the equation:

\[ -27 + k = 0 \]

### Step 6: Solve for \( k \)
To find \( k \), add \( 27 \) to both sides:

\[ k = 27 \]

### Final Answer
Thus, the value of \( k \) is \( 27 \).