Question

If α and β are the zero of 2x² + 5x − 8, then the value of (αβ) is

(a) $\frac{-5}{2}$
(b) $\frac{5}{2}$
(c) $\frac{-9}{2}$
(d) $\frac{9}{2}$

Answer 1

$$\begin{gathered} \left(\text{c}\right)\frac{-9}{2} \\ \text{Given:}\alpha \text{and}\beta \text{are the zeroes of}2x^2+5x-9. \\ \mathrm{If}\alpha \mathrm{and}\beta \mathrm{are}\mathrm{the}\mathrm{zeroes},\mathrm{then}{x}^2-(\alpha +\beta )x+\alpha \beta \mathrm{is}\mathrm{the}\mathrm{required}\mathrm{polynomial}. \\ \mathrm{The}\mathrm{polynomial}\mathrm{will}\mathrm{be}{x}^2-\frac{5}{2}x-\frac{9}{2}. \\ \text{∴}\alpha \beta \text{=}\frac{-9}{2} \end{gathered}$$