1. The problem statement, all variables and given/known data Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) 2. Relevant equations (a+bi)*(a-bi) = a^2 + b^2 where a, and b are always reals? Not really sure if this helps or not. 3. The attempt at a solution I'm really clueless on how to start approaching this. I was thinking perhaps the fundamental theorem of algebra might be of some use, or perhaps the fact that a number of complex form multiplied by it's conjugate is a real number, but I'm really not sure. Could anyone give me a nudge in the right direction? Any help would be greatly appreciated!! Thanks!