Suppose we are given that $a+b+c = A $, $ab+bc+ca = B$ , $abc = C$ , We can observe that if we solve by eliminating two variables out of three(a,b,c) from three equations we would end up getting $x^3 - Ax^2 +Bx -C =0$ a cubic equation which is satisfied by the last one not eliminated,
- So if we do the same with a cubic equation with two roots equal and going backwards we would have two variables and three equations so in general for a cubic equation whose roots we know are supposed to be having a double root can be easily solved as compared to the ones which are distinct in general ?
- So without cardano reduction stuff we can solve for all roots in this special equal roots case (double) easily ?