Section 4.4

# Section 4.4 - Section 4.4 Theorems About Zeros of...

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Section 4.4 Theorems About Zeros of Polynomial Functions The Fundamental Theorem of Algebra Every polynomial function of degree n, with n 1, has at least one zero in the set of complex numbers. Every polynomial function f of degree n, with n 1, can be factored into n linear factors (not necessarily unique): that is, f(x) = a n (x - c 1 ) (x - c 2 ) . . . (x - c n ). Recall, if c is a zero of a polynomial then x - c is a factor of the polynomial. Find a polynomial of degree 3 with the given numbers as zeros. - 2, 3, 5 - 3, 2i, - 2i - 4, - 1 - , - 1 + Find a polynomial of degree 5 with - 1 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 1 as a zero of multiplicity 1. If a complex number a + bi, b 0 is a zero of a polynomial function f(x) with real coefficients, then its conjugate, a - bi is also a zero. If a + c is a zero of a polynomial function f(x) with rational coefficients, then its conjugate a - c is also a zero. Suppose that a polynomial function of degree 4

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## This note was uploaded on 10/12/2011 for the course MATH 1513 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Section 4.4 - Section 4.4 Theorems About Zeros of...

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