If α, β, γ are the zeros of the polynomial
Question:

If $\alpha, \beta, \gamma$ are the zeros of the polynomial $2 x^{3}+x^{2}-13 x+6$, then $\alpha \beta y=?$

(a) −3
(b) 3

(c) $\frac{-1}{2}$

(d) $\frac{-13}{2}$

Solution:

(a) $-3$

Since $\alpha, \beta$ and $\gamma$ are the zeroes of $2 x^{3}+x^{2}-13 x+6$, we have:

$\alpha \beta \gamma=\frac{-(\text { constant term })}{\text { co-efficient of } x^{3}}=\frac{-6}{2}=-3$