If roots of `7x^(2) - 11 x + k = 0, k ne 0` are reciprocal of each other, then k is equal to

Options

A. `-1`
B. `7//1`
C. 7
D. `11/7`

Answer

To solve the problem, we need to find the value of \( k \) such that the roots of the quadratic equation \( 7x^2 - 11x + k = 0 \) are reciprocals of each other.

### Step-by-Step Solution:

1. **Understanding the Roots**:
Let the roots of the equation be \( \alpha \) and \( \beta \). Since the roots are reciprocals, we can say that \( \beta = \frac{1}{\alpha} \).

2. **Using the Product of Roots**:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the product of the roots is given by:
\[ \alpha \cdot \beta = \frac{c}{a} \]
Here, \( a = 7 \), \( b = -11 \), and \( c = k \). Therefore, we can write:
\[ \alpha \cdot \beta = \frac{k}{7} \]

3. **Substituting the Roots**:
Since \( \beta = \frac{1}{\alpha} \), we can substitute this into the product of the roots:
\[ \alpha \cdot \frac{1}{\alpha} = 1 \]
Thus, we have:
\[ 1 = \frac{k}{7} \]

4. **Solving for \( k \)**:
To find \( k \), we can rearrange the equation:
\[ k = 7 \cdot 1 = 7 \]

5. **Conclusion**:
Therefore, the value of \( k \) is \( 7 \).

### Final Answer:
\[ k = 7 \]