I would like to know if it is possible to select R1, R2, R3, C1, and C2 such that the quadratic equation yields complex roots.
$s_{1,2}=-\frac{b\pm \sqrt{b^2-4ac}}{2a}$
where
$a = R_{1}R_{2}R_{3}C_{1}C_{2}$
$b = R_{1}C_{1}(R_{2}+R_{3})+R_{3}C_{2}(R_{1}+R_{2})$
$c = R_{1}+R_{2}+R_{3}$
Obviously this depends solely on $b^2-4ac$. With 6 variables, even with maximum factoring and simplification, it is difficult to see whether 4a can be made greater than $b^2$. Is there a rule/theory/theorem which I can turn to in order to prove whether there exists any combination of the six variables that would have $4ac>b^2$?
Thanks,
Jason