Complex conjugate root theorem
Theorem that complex roots of a real polynomial come in conjugate pairs
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 being 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 proved by using the intermediate value theorem.
Nº Q5156572 ★
Common · Knowledge
Complex conjugate root theorem
Theorem that complex roots of a real polynomial come in conjugate pairs
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 being 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 proved by using the intermediate value theorem.
From Wikipedia
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 being 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 proved by using the intermediate value theorem.
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
-
G
Gauss–Lucas theorem
Geometric relation between the roots of a polynomial and those of its derivative
Nº Q1008566 ★
Not listed
-
Polynomial root
Element at which the polynomial evaluates to zero
Nº Q20113351 ★★
Not listed
-
Complex conjugate
Operation on complex numbers in which the sign of the real part is kept but the sign of the imaginary part is reversed
Nº Q381040 ★★
Not listed
-
Absolute value of a complex number
Distance of a complex number from the origin in the complex plane
Nº Q3317982 ★★
Not listed
-
P
Polynomial remainder theorem
Theorem
Nº Q1071948 ★★
Not listed
-
I
Identity theorem
Theorem that an analytic function is completely determined by its values on a countable subset that contains a converging sequence together with its limit
Nº Q1038716 ★
Not listed