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. **Let the Roots be Defined**:
Let one root be \( r \). Since one root is the reciprocal of the other, the other root will be \( \frac{1}{r} \).

2. **Sum of the Roots**:
According to Vieta's formulas, the sum of the roots of the quadratic equation \( ax^2 + bx + c = 0 \) is given by:
\[ \text{Sum of roots} = -\frac{b}{a} \]
For our equation \( 3x^2 - 10x + k = 0 \), we have \( a = 3 \) and \( b = -10 \). Thus, the sum of the roots is:
\[ r + \frac{1}{r} = -\frac{-10}{3} = \frac{10}{3} \]

3. **Product of the Roots**:
The product of the roots is given by:
\[ \text{Product of roots} = \frac{c}{a} \]
In our case, this gives:
\[ r \cdot \frac{1}{r} = \frac{k}{3} \]
Since \( r \cdot \frac{1}{r} = 1 \), we have:
\[ 1 = \frac{k}{3} \]

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

### Conclusion:
Thus, the value of \( k \) is \( 3 \).