Question

If the roots of the equation px² + x + r = 0 are reciprocal to each other, then which one of the following is correct?

• A. p = 2r
• B. p = r
• C. 2p = r
• D. p = 4r

Answer 1

The Correct Option is A

For reciprocal roots, if \( \alpha \) and \( \beta \) are the roots, then \( \alpha \times \beta = 1 \). From *Vieta’s formulas*, \[ \alpha + \beta = -\frac{1}{p} \text{ and } \alpha \beta = \frac{1}{p}. \]. Because \( \alpha \times \beta = 1 \), we conclude that \( \mathbf{p = r} \).