If 3 is the root of the equation `x^(2) - 8x + k = 0`. Then what is the value of k ?

Options

A. `-15`
B. 9
C. 15
D. 24

Answer

To find the value of \( k \) in the quadratic equation \( x^2 - 8x + k = 0 \) given that 3 is a root, we can follow these steps:

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

\[ 3^2 - 8(3) + k = 0 \]

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

\[ 3^2 = 9 \]

### Step 3: Calculate \( -8(3) \)
Now calculate \( -8(3) \):

\[ -8(3) = -24 \]

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

\[ 9 - 24 + k = 0 \]

### Step 5: Simplify the equation
Combine the constants:

\[ -15 + k = 0 \]

### Step 6: Solve for \( k \)
To find \( k \), add 15 to both sides:

\[ k = 15 \]

Thus, the value of \( k \) is \( 15 \).

### Final Answer
The value of \( k \) is \( 15 \).

---