Theorem of Roots

The Theorem of Roots states that a polynomial equation of degree \( n \) (where the highest exponent is \( n \)) has exactly \( n \) solutions, called roots, if you count complex and repeated roots. These roots are the values of the variable that make the polynomial equal to zero. For example, a quadratic (degree 2) has two roots, which can be real or complex. This theorem guarantees that all solutions exist within the complex number system, providing a complete understanding of where the polynomial equals zero.