# Sum of Roots and Product of Roots

Example

The roots of $2{x}^{2}+3x-1=0$   are $\alpha$  and $\beta$ .  Find the values of
(a) $\left(\alpha +1\right)\left(\beta +1\right)$
(b) $\frac{1}{\alpha }+\frac{1}{\beta }$
(c) ${\alpha }^{2}\beta +\alpha {\beta }^{2}$
(d) $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$
[Clue: $α 2 + β 2 = (α+β) 2 −2αβ$   ]