Suppose that f R[x] and that C such that f() = 0. Let be the complex conjugate of . Show that f() = 0 as well.

Suppose that f ∈ R[x] and that α ∈ C such that f(α) = 0. Let ¯α be the complex

conjugate of α. Show that f(¯α) = 0 as well.

Prove that the Fundamental Theorem of Algebra is equivalent to the assertion that

every nonconstant polynomial in R[x] is a product of linear and quadratic factors with

real coefficients.