5-6 The Fundamental Theorem of Algebra

Objective

To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions

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You can factor any polynomial of degree n into n linear factors, but sometimes the factors will involve imaginary numbers.

Essential Understanding The degree of a polynomial equation tells you how many roots the equation has.

It is easy to see graphically that every polynomial function of degree 1 has a single zero, the x-intercept. However, there appear to be three possibilities for polynomials of degree 2. They correspond to these three graphs:

y = x 2 − 4 y equals , x squared , minus 4  Two real zeros

y = x 2 − 2 x + 1 y equals , x squared , minus 2 x plus 1  One real zero

y = x 2 + 2 x + 2 y equals , x squared , plus 2 x plus 2  No real zeros

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