An algebraic approach to the Fundamental Theorem of Algebra

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In this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real-closed fields and quadratic forms. We show, by means of Galois theory, that F(-1) is algebraically closed if F is real-closed. Lastly, we explain the algebraic closure of R(-1)=C by demonstrating the real-closeness of R.