Question

If one zero of 3x² + 8x + k be the reciprocal of the other, then k = ?

(a) 3
(b) −3
(c) $\frac{1}{3}$
(d) $\frac{-1}{3}$

Answer 1

$$\begin{gathered} \left(\text{a}\right)k=3 \\ \text{Let}\alpha \text{and}\frac{1}{\alpha }\text{be the zeroes of 3}{x}^2-8x+k. \\ \text{Then product of zeroes=}\frac{k}{3} \\ =>\alpha \times \frac{1}{\alpha }=\frac{k}{3} \\ =>1=\frac{k}{3} \\ =>k=3 \end{gathered}$$