CAT 2015 Quantitative Ability

${\mathit{x}}^2+\mathit{r}\mathit{x}+\mathit{s}=0$
r = - (sum of roots) r = -ve
s = product of roots s = +ve
s - r = +ve
r + s + 1
= -a-b + ab + 1 (where a & b are roots)
= (a -1) (b-1) = +ve
$\Rightarrow \frac{+\mathit{v}\mathit{e}}{+\mathit{v}\mathit{e}}=+\mathit{v}\mathit{e}$
Alternative Method:
Take roots as 2,2
=>r = - 4 & s = 4
$\Rightarrow \frac{\mathit{r}+\mathit{s}+1}{\mathit{s}-\mathit{r}}=\frac{1}{8}=+\mathit{v}\mathit{e}$