# If α and β are the zero of

Question:

If $\alpha$ and $\beta$ are the zero of $2 x^{2}+5 x-8$, then the value of $(\alpha \beta)$ is

(a) $\frac{-5}{2}$

(b) $\frac{5}{2}$

(c) $\frac{-9}{2}$

(d) $\frac{9}{2}$

Solution:

(c) $\frac{-9}{2}$

Given: $\alpha$ and $\beta$ are the zeroes of $2 x^{2}+5 x-9$

If $\alpha$ and $\beta$ are the zeroes, then $x^{2}-(\alpha+\beta) x+\alpha \beta$ is the required polynomial.

The polynomial will be $x^{2}-\frac{5}{2} x-\frac{9}{2}$.

$\therefore \alpha \beta=\frac{-9}{2}$