Roots of a polynomial with irrational coefficients

$\begingroup$

I know about algebraic numbers and transcendental numbers. How the roots of a polynomial with irrational coefficients are classified. Are they transcendental?

$\endgroup$ 2

1 Answer

$\begingroup$

The roots of a polynomial with algebraic coefficients are all algebraic, and a monic polynomial whose roots are all algebraic has algebraic coefficients.

So a monic polynomial with some transcendental coefficient must have at least one transcendental root (and vice versa), but it can also have algebraic roots (for example, $0$ is a non transcendental root of $X^2- \pi X = 0$).

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy