If one root of the quadratic equation `3x^(2)-10x+k=0` is reciprocal of the other, find the value of k.

Answer

To solve the problem, we need to find the value of \( k \) in the quadratic equation \( 3x^2 - 10x + k = 0 \) given that one root is the reciprocal of the other.

### Step-by-step Solution:

1. **Understanding the Roots**:
Let the roots of the quadratic equation be \( \alpha \) and \( \frac{1}{\alpha} \). This means that one root is the reciprocal of the other.

2. **Using the Product of Roots Formula**:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the product of the roots is given by:
\[ \alpha \cdot \frac{1}{\alpha} = \frac{c}{a} \]
Here, \( c = k \) and \( a = 3 \) (from the equation \( 3x^2 - 10x + k = 0 \)).

3. **Setting Up the Equation**:
Since \( \alpha \cdot \frac{1}{\alpha} = 1 \), we can equate this to the product of the roots:
\[ 1 = \frac{k}{3} \]

4. **Solving for \( k \)**:
To find \( k \), we multiply both sides of the equation by 3:
\[ k = 3 \cdot 1 = 3 \]

5. **Conclusion**:
Therefore, the value of \( k \) is \( 3 \).

### Final Answer:
The value of \( k \) is \( 3 \).