just making notes on finding roots of quartics etc with complex numbers, are these statements correct:?
1. (z-(x))(z-(y)) - where x and y are roots of the equation , expanding this will give you the original equation, 3 brackets for cubic and 4 for quartic.
2. (z-x) ( y ) - X is a known root of the equation, where Y is an unknown factor of the equation, you calculate Y based on the original equation and the given root, and then if Y is a quadratic you solve for 2 roots.
so if i know the roots but not the equation, i use method 1 , if i know the equation but not the roots i use method 2?
are these statements entirely correct as i dont want to write it down if its a bit wrong