For equal root , `x^2-6x+k` value of k is

Options

A. 9
B. 3
C. 2
D. 8

Answer

To find the value of \( k \) for which the quadratic equation \( x^2 - 6x + k \) has equal roots, we follow these steps:

### Step 1: Understand the condition for equal roots
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the roots are equal if the discriminant is equal to zero. The discriminant \( D \) is given by the formula:
\[ D = b^2 - 4ac \]

### Step 2: Identify the coefficients
In the equation \( x^2 - 6x + k \):
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -6 \) (coefficient of \( x \))
- \( c = k \) (constant term)

### Step 3: Set up the discriminant equation
We set the discriminant equal to zero for equal roots:
\[ D = b^2 - 4ac = 0 \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ (-6)^2 - 4 \cdot 1 \cdot k = 0 \]

### Step 4: Simplify the equation
Calculating \( (-6)^2 \):
\[ 36 - 4k = 0 \]

### Step 5: Solve for \( k \)
Rearranging the equation gives:
\[ 36 = 4k \]
Dividing both sides by 4:
\[ k = \frac{36}{4} = 9 \]

### Conclusion
The value of \( k \) for which the quadratic equation \( x^2 - 6x + k \) has equal roots is:
\[ \boxed{9} \]