Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed.

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Presentation transcript:

Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed as the product of n linear factors. Hence, P(x) has exactly n zeros, not necessarily distinct. The Fundamental Theorem of Algebra

Find all zeros. Write the polynomial as the product of linear factors.

Find all zeros. Factor the polynomial as the product of linear factors.

If a polynomial P(x) has real coefficients, and if a+bi is a zero of P(x), then its complex conjugate a-bi is also a zero of P(x) Complex Conjugate Zeros Theorem Find all remaining zeros given the information provided. Degree: 5, 2-4i and 3 and 7i are zeros 2+4i and -7i are also zeros

Given a zero of the polynomial, determine all other zeros and write the polynomial as the product of linear factors Conjugates

ZEROS HOMEWORK: Read , p odd

HOMEWORK Pages 388; 1-21 odd