Consider a function, $f:\mathbb{R}\rightarrow \mathbb{R},\:f\left(x\right)=x^4+ax^3+bx^2$ where $a,b\in \mathbb{Z}\setminus \left\{0\right\}$ and $b\ne \left(\frac{a}{2}\right)^2$ with three distinct real roots whose roots and stationary points have integer $x$ coordinates. Generalise such a function, $f(x)$.
I've asked this exact same question here previously, but now I would like to know how to write a piece of pseudocode that could provide a solution for it.
I'm practicing pseudocode currently and it would be really cool if anyone here could help! :)