Prove the following: Let f(x) be a polynomial in R[x] of positive degree n. 1. The...

Prove the following:

Let f(x) be a polynomial in R[x] of positive degree n.

1. The polynomial f(x) factors in R[x] as the product of polynomials of degree
1 or 2.

2. The polynomial f(x) has n roots in C (counting multiplicity). In particular,
there are non-negative integers r and s satisfying r+2s = n such that
f(x) has r real roots and s pairs of non-real conjugate complex numbers as
roots.

3. The polynomial f(x) factors in C[x] as the product of n degree-one polynomials.

Expert Solution

Colby Messinger answered 2 years ago

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Prove the following: Let f(x) be a polynomial in R[x] of positive degree n. 1. The...

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