If one zero of ` 3x^(2) + 8x + k` be the reciprocal of the other then k = ?

Options

A. 3
B. `-3`
C. ` 1/3`
D. `(-1)/3`

Explanation

To solve the problem where one zero of the quadratic polynomial \(3x^2 + 8x + k\) is the reciprocal of the other, we can follow these steps:

### Step-by-Step Solution

1. **Let the Zeros be \( \alpha \) and \( \beta \):**
Given that one zero is the reciprocal of the other, we can write:
\[ \alpha = \frac{1}{\beta} \]

2. **Product of the Zeros:**
The product of the zeros of the polynomial \(ax^2 + bx + c\) is given by:
\[ \alpha \beta = \frac{c}{a} \]
For the polynomial \(3x^2 + 8x + k\), we have:
\[ \alpha \beta = \frac{k}{3} \]

3. **Using the Reciprocal Relationship:**
Since \( \alpha = \frac{1}{\beta} \), we can substitute \( \alpha \) in the product equation:
\[ \left(\frac{1}{\beta}\right) \beta = \frac{k}{3} \]
Simplifying this, we get:
\[ 1 = \frac{k}{3} \]

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

Thus, the value of \( k \) is \( \boxed{3} \).