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We use the Fundamental Theorem. Of Algebra, Descartes Rule of Signs and the Complex Conjugate Theorem. to predict the nature of the roots of a polynomial.
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Setting the Factors of a Polynomial Expression equal to zero gives the Solutions to the Equation when the polynomial expression equals zero. Another name for the Solutions of a Polynomial is the Roots of a Polynomial !
In a Polynomial Equation, two polynomials are set equal to each other.