Suppose I am given this equation : $x^2 - 12x - 28$ = 0.
Using the rational root theorem, I find that the possible rational roots are ( if I am correct):
$$1/1, 2/1,7/1,14/,28/1$$ or their additive inverses.
I try the number $(-2)$ and I observe it works.
At this stage, knowing one solution of the quadratic trinomial , is there any rule allowing me to determine the second root in terms of the first, or, at least, a rule allowing me to eliminate some candidates in the list above?
I mean, is there some general law stating a relation between the roots of a quadratic trinomial?