If roots of equation `2x^2 - 8x + c=0` are equal . Then the value of c will be

Options

A. 2
B. 4
C. 6
D. 8

Answer

To find the value of \( c \) for which the roots of the equation \( 2x^2 - 8x + c = 0 \) are equal, we need to use the concept of the discriminant. The roots of a quadratic equation are equal when the discriminant is zero.

### Step-by-step Solution:

1. **Identify the coefficients**:
The given quadratic equation is \( 2x^2 - 8x + c = 0 \). Here, the coefficients are:
- \( a = 2 \)
- \( b = -8 \)
- \( c = c \) (the constant term we need to find)

2. **Write the formula for the discriminant**:
The discriminant \( D \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by:
\[ D = b^2 - 4ac \]

3. **Set the discriminant to zero**:
For the roots to be equal, we set the discriminant \( D \) to zero:
\[ D = 0 \]

4. **Substitute the values of \( a \), \( b \), and \( c \)**:
Substitute \( a = 2 \), \( b = -8 \), and \( c = c \) into the discriminant formula:
\[ 0 = (-8)^2 - 4 \cdot 2 \cdot c \]

5. **Calculate \( (-8)^2 \)**:
\[ 0 = 64 - 8c \]

6. **Rearrange the equation**:
Move \( 8c \) to the other side:
\[ 8c = 64 \]

7. **Solve for \( c \)**:
Divide both sides by 8:
\[ c = \frac{64}{8} = 8 \]

### Final Answer:
Thus, the value of \( c \) for which the roots of the equation are equal is:
\[ \boxed{8} \]