Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematik-Online problems:

Problem 9: Complex Roots of Polynomials


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


a)
Given the polynomials $ p(z)=z^4+a_3z^3+a_2z^2+a_1z+a_0$, with $ a_0,\,\ldots , a_4\in\ \mathbb{R}$. Proof: Is $ z\in\mathbb{C}$ a root of $ p$, then the complex conjugate $ \bar{z}$ is a root of $ p$, too.
b)
Find all roots of $ p(z)=z^4+z^3+2z^2+z+1$. Hint: $ p({\mathrm{i}})=0$.
c)
Find all roots of $ q(z)=
z^5+z^4-13z^3+19z^2-68z+60$.

(Authors: Kimmerle/Roggenkamp/Höfert)

see also:


[Solutions]

  automatisch erstellt am 14. 10. 2004