If x^(2) - 4x + a = 0 root are equal, then a =

Options

A. `-4`
B. 8
C. `-8`
D. 4

Answer

To find the value of \( a \) such that the roots of the equation \( x^2 - 4x + a = 0 \) are equal, we will use the condition for equal roots in a quadratic equation. The condition states that the discriminant must be equal to zero.

### Step-by-step Solution:

1. **Identify the coefficients**:
The given quadratic equation is in the form \( ax^2 + bx + c = 0 \).
Here, \( a = 1 \), \( b = -4 \), and \( c = a \).

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

3. **Substitute the coefficients into the discriminant**:
Substitute \( a = 1 \), \( b = -4 \), and \( c = a \) into the discriminant formula:
\[ D = (-4)^2 - 4 \cdot 1 \cdot a \]

4. **Simplify the expression**:
Calculate \( D \):
\[ D = 16 - 4a \]

5. **Set the discriminant equal to zero**:
For the roots to be equal, set the discriminant \( D \) to zero:
\[ 16 - 4a = 0 \]

6. **Solve for \( a \)**:
Rearranging the equation gives:
\[ 4a = 16 \]
Dividing both sides by 4:
\[ a = 4 \]

### Final Answer:
Thus, the value of \( a \) is \( 4 \).

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