3.6 complex zereos. the fundamental theorem of algebra the fundamental theorem of algebra says that...
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3.6 Complex Zereos
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The Fundamental Theorem of Algebra
• The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have at least one complex zero.
• Remember real numbers like 7 can be considered complex when written as 7 + 0i. So any polynomial will have complex zeros.
• The degree of the polynomial tells you exactly how many complex roots exist
• Even degree polynomials may have no real roots while odd degree must have one real root.
• Remember, Imaginary roots exist in pairs.
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The Complete Factorization Theorem
• The Complete Factorization Theorem states that for any polynomial with degree 1 or greater the polynomial can be written as P(x) = a(x – c1) (x – c2) (x – c3) .... (x – cn) where a and c1, c2, c3, ... cn are complex numbers.
• This means that a polynomial can be written in factored form.
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