If a + bi is a root of a real polynomial, then so is a − bi
In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.[1]
It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must have at least one real root.[2] That fact can also be proved by using the intermediate value theorem.
^Anthony G. O'Farell and Gary McGuire (2002). "Complex numbers, 8.4.2 Complex roots of real polynomials". Maynooth Mathematical Olympiad Manual. Logic Press. p. 104. ISBN 0954426908. Preview available at Google books
^Alan Jeffrey (2005). "Analytic Functions". Complex Analysis and Applications. CRC Press. pp. 22–23. ISBN 158488553X.
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