If 3 is a root of the equation `kx^2 - kx - 3 = 0`, then the value of k is ...........

Options

A. 3
B. `1//2`
C. 4
D. 2

Answer

To find the value of \( k \) such that \( 3 \) is a root of the equation \( kx^2 - kx - 3 = 0 \), 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:
\[ k(3^2) - k(3) - 3 = 0 \]

### Step 2: Simplify the equation
Now, simplify the left-hand side:
\[ k(9) - k(3) - 3 = 0 \]
This simplifies to:
\[ 9k - 3k - 3 = 0 \]

### Step 3: Combine like terms
Combine the terms involving \( k \):
\[ (9k - 3k) - 3 = 0 \]
This results in:
\[ 6k - 3 = 0 \]

### Step 4: Solve for \( k \)
Now, isolate \( k \):
\[ 6k = 3 \]
\[ k = \frac{3}{6} \]
\[ k = \frac{1}{2} \]

### Conclusion
Thus, the value of \( k \) is:
\[ \boxed{\frac{1}{2}} \]

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