Statement -1 In the equation `ax^(2)+3x+5=0`, if one root is reciprocal of the other, then `a` is equal to 5.
Statement -2 Product of the roots is 1.

Options

A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1
B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true

Explanation

To solve the problem, we need to analyze the quadratic equation given and determine the conditions under which one root is the reciprocal of the other.

### Step-by-Step Solution:

1. **Understanding the Equation**:
We start with the quadratic equation given:
\[ ax^2 + 3x + 5 = 0 \]
where \( a \) is a coefficient that we need to determine.

2. **Reciprocal Roots Condition**:
If one root is the reciprocal of the other, we can denote the roots as \( \alpha \) and \( \beta \). The condition for reciprocal roots is:
\[ \alpha \cdot \beta = 1 \]

3. **Using Vieta's Formulas**:
According to Vieta's formulas for a quadratic equation \( ax^2 + bx + c = 0 \):
- The sum of the roots \( \alpha + \beta = -\frac{b}{a} \)
- The product of the roots \( \alpha \cdot \beta = \frac{c}{a} \)

For our equation:
- \( b = 3 \)
- \( c = 5 \)

Therefore, the product of the roots is:
\[ \alpha \cdot \beta = \frac{5}{a} \]

4. **Setting the Product Equal to 1**:
Since we know that \( \alpha \cdot \beta = 1 \) (because they are reciprocal), we can set up the equation:
\[ \frac{5}{a} = 1 \]

5. **Solving for \( a \)**:
To find \( a \), we multiply both sides of the equation by \( a \):
\[ 5 = a \]

6. **Conclusion**:
Thus, we find that:
\[ a = 5 \]

### Final Verification:
- If \( a = 5 \), the equation becomes:
\[ 5x^2 + 3x + 5 = 0 \]
- The product of the roots is:
\[ \alpha \cdot \beta = \frac{5}{5} = 1 \]
- This confirms that the roots are indeed reciprocal.