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

Explanation

To find the value of \( k \) in the 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 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 \( -8(3) \)
Calculate \( -8(3) \):

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

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

\[ 9 - 24 + k = 0 \]

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

\[ 9 - 24 = -15 \]

So the equation becomes:

\[ -15 + k = 0 \]

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

\[ k = 15 \]

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

\[ \boxed{15} \]

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