The proof of the fundamental theorem of algebra using the Brouwer fixed point theorem is given here:
B.H. Arnold, "A topological proof of the fundamental theorem of algebra" Amer. Math. Monthly , 56 (1949) pp. 465–466
The proof of the fundamental theorem of algebra using the Brouwer fixed point theorem is given here:
B.H. Arnold, "A topological proof of the fundamental theorem of algebra" Amer. Math. Monthly , 56 (1949) pp. 465–466