problem 2 of Indian Mathematical Olympiad 1989
Source: Roots of a polynomial real or non real
September 1, 2009
algebrapolynomialVietaalgebra unsolved
Problem Statement
Let and be any four real numbers, not all equal to zero. Prove that the roots of the polynomial f(x) \equal{} x^{6} \plus{} ax^{3} \plus{} bx^{2} \plus{} cx \plus{} d can't all be real.