The roots of the equation `ax^(2)+bx+c=0` will be reciprocal of each other if

Options

A. `a=b`
B. `b=c`
C. `c=a`
D. None of these

Explanation

To determine the condition under which the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are reciprocals of each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Roots**:
Let the roots of the quadratic equation \( ax^2 + bx + c = 0 \) be \( \alpha \) and \( \beta \). For the roots to be reciprocals of each other, we need \( \alpha \cdot \beta = 1 \).

2. **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 \( \alpha \cdot \beta = \frac{c}{a} \)

3. **Setting the Product of Roots to 1**:
Since we want the roots to be reciprocals, we set the product of the roots equal to 1:
\[ \alpha \cdot \beta = 1 \]
From Vieta's, we have:
\[ \frac{c}{a} = 1 \]

4. **Deriving the Condition**:
Rearranging the equation \( \frac{c}{a} = 1 \) gives:
\[ c = a \]

5. **Conclusion**:
Therefore, the condition for the roots of the quadratic equation \( ax^2 + bx + c = 0 \) to be reciprocals of each other is:
\[ c = a \]