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.
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. That fact can also be proven by using the intermediate value theorem.
Read more about Complex Conjugate Root Theorem: Examples and Consequences, Simple Proof
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