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Polynomial Equations and Inequalities

Video Summary:

Methods for solving quadratic equations known to ancient civilizations 16th century mathematicians derived formulas to solve third and fourth degree equations In 1824, Norwegian mathematician Niels Henrik Abel proved it impossible to find a formula to solve fifth degree equations Also true for equations of degree greater than five. If n is a positive integer, k a nonzero complex number, then a solution of xn = k is called an nth root of k. Complex nth Roots Theorem If n is a positive integer and k is a nonzero complex number, then the equation xn = k has exactly n complex roots.

 


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