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
Famous quotes containing the words complex, root and/or theorem:
“In ordinary speech the words perception and sensation tend to be used interchangeably, but the psychologist distinguishes. Sensations are the items of consciousness—a color, a weight, a texture—that we tend to think of as simple and single. Perceptions are complex affairs that embrace sensation together with other, associated or revived contents of the mind, including emotions.”
—Jacques Barzun (b. 1907)
“To those who despair of everything reason cannot provide a faith, but only passion, and in this case it must be the same passion that lay at the root of the despair, namely humiliation and hatred.”
—Albert Camus (1913–1960)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)