Assertion (A) : The equation `8x^(2)+3kx+2=0` has equal roots than the value of k is `+-(8)/(3)`.
Reason (R ): The equation `ax^(2)+bx+c=0` has equal roots if `D=b^(2)-4ac=0`.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false
D. A is false but R is true

Answer

To solve the problem, we need to determine the value of \( k \) for which the quadratic equation \( 8x^2 + 3kx + 2 = 0 \) has equal roots. We will use the discriminant condition for equal roots.

### Step-by-Step Solution:

1. **Identify the coefficients**:
The given quadratic equation is in the form \( ax^2 + bx + c = 0 \), where:
- \( a = 8 \)
- \( b = 3k \)
- \( c = 2 \)

2. **Use the discriminant condition**:
For the quadratic equation to have equal roots, the discriminant \( D \) must be equal to zero. The discriminant is given by:
\[ D = b^2 - 4ac \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ D = (3k)^2 - 4 \cdot 8 \cdot 2 \]

3. **Calculate the discriminant**:
\[ D = 9k^2 - 64 \]

4. **Set the discriminant to zero**:
For equal roots, we set the discriminant \( D \) to zero:
\[ 9k^2 - 64 = 0 \]

5. **Solve for \( k^2 \)**:
Rearranging the equation gives:
\[ 9k^2 = 64 \]
Dividing both sides by 9:
\[ k^2 = \frac{64}{9} \]

6. **Take the square root**:
Taking the square root of both sides gives:
\[ k = \pm \frac{8}{3} \]

### Final Answer:
The values of \( k \) for which the equation \( 8x^2 + 3kx + 2 = 0 \) has equal roots are:
\[ k = \frac{8}{3} \quad \text{and} \quad k = -\frac{8}{3} \]