If the difference of the roots of `x^(2)-lamdax+8=0` be 2 the value of `lamda` is

Options

A. a) `+-2`
B. b) `+-4`
C. c) `+-6`
D. d) `+-8`

Answer

To solve the problem, we need to find the value of \( \lambda \) such that the difference of the roots of the quadratic equation \( x^2 - \lambda x + 8 = 0 \) is equal to 2.

### Step-by-Step Solution:

1. **Identify the Quadratic Equation:**
The given equation is:
\[ x^2 - \lambda x + 8 = 0 \]

2. **Identify Coefficients:**
We can compare this with the standard form of a quadratic equation \( ax^2 + bx + c = 0 \). Here, we have:
- \( a = 1 \)
- \( b = -\lambda \)
- \( c = 8 \)

3. **Use the Formula for the Difference of Roots:**
The formula for the difference of the roots \( r_1 \) and \( r_2 \) of a quadratic equation is given by:
\[ \text{Difference of roots} = \frac{\sqrt{b^2 - 4ac}}{a} \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ \text{Difference of roots} = \frac{\sqrt{(-\lambda)^2 - 4 \cdot 1 \cdot 8}}{1} = \sqrt{\lambda^2 - 32} \]

4. **Set the Difference of Roots Equal to 2:**
According to the problem, the difference of the roots is equal to 2:
\[ \sqrt{\lambda^2 - 32} = 2 \]

5. **Square Both Sides:**
To eliminate the square root, we square both sides:
\[ \lambda^2 - 32 = 4 \]

6. **Solve for \( \lambda^2 \):**
Rearranging the equation gives:
\[ \lambda^2 = 4 + 32 = 36 \]

7. **Find \( \lambda \):**
Taking the square root of both sides, we find:
\[ \lambda = \pm 6 \]

### Final Answer:
Thus, the value of \( \lambda \) is:
\[ \lambda = \pm 6 \]