I need help to plot the graph of following equation with the conditions given below

$\displaystyle F(\pi)$ =(a $\displaystyle \pi $*$\displaystyle \pi $+b $\displaystyle \pi $+$\displaystyle c$)/( d$\displaystyle \pi$*$\displaystyle \pi$ +e $\displaystyle \pi $+$\displaystyle f$)

where $\displaystyle \alpha$ & $\displaystyle \beta$ are roots of denominator.. and $\displaystyle \gamma$ & $\displaystyle \theta$ are roots of numerator

(i) $\displaystyle \alpha $ < $\displaystyle \gamma$ < $\displaystyle \beta$ < $\displaystyle \theta$

(ii)$\displaystyle \alpha = \beta$ & $\displaystyle \gamma $$\displaystyle =$$\displaystyle \theta$ & $\displaystyle \alpha < \gamma$

(iii) all the roots are imaginary

(iv) numerator has no roots

(v) denominator has no roots

i don't need the answers... i really need the method(Logic)

If there are any short cuts.. please tell me

answer me at the earliest