I'm struggling to find a real life practical reason for why one would want to use the roots of an existing polynomial as the basis for constructing another polynomial. Eg if roots of existing cubic are a,b,c say, find a polynomial with roots 2a+1, 2b+1, 2c+1. Great as an intellectual exercise but of what use in the real world (by which I don't mean postgraduate theoretical pure maths!) The best thing I can come up with is some kind of handwaving mutterings about 'cryptography' which to be honest I have no idea if that is true or not! Anyone got a real reason?