Problems(1)
One day, Ivan was imprisoned by an evil king. The evil king said : "If you can correctly determine the
polynomial that I'm thinking of, you'll be free. If after 2014 tries, you can't guess it, you'll be executed."
Ivan answered : "Are there any clues?" The evil king replied : "I can tell you that the polynomial has
real coefficients and is monic. Furthermore, all roots are positive real numbers." That night, a kind
wizard, told him the polynomial. The conversation was heard by the king who was visiting Ivan. He
killed the wizard. The next day, Ivan forgot the polynomial, except that the coefficients of x2013 is 2014,
and that the constant term is 1. Can Ivan guarantee freedom? And if so, in how many tries? (Assume
that Ivan is very unlucky so any random guess fails.) algebrapolynomial