I have a quartic polynomial in $x$ (too long to write here)
$f(x,c_1, c_2, c_2)$
where $c_1, c_2, c_3$ are constants which I have complete freedom over how to fix their values, as long as they are all greater than zero.
As this is a quartic, I have 4 roots to $f=0$ (two are usually imaginary and two real). I want to fix my constants so that I have two real, positive values of $x$.
At the moment I'm just plotting $f(x)$ with different values of $c_1, c_2, c_3$ and trying to pick these values so that my graph crosses the real positive axis twice. However so far I am unsuccessful.
Is there some analytical method of doing this?