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3.4 Übungen

(Unterschied zwischen Versionen)

Version vom 13:41, 10. Mär. 2009

Übungen

Carry out the following divisions (not all are exact, i.e. have no remainder)

a)	x−1x2−1	b)	x2x+1	c)	x+ax3+a3
d)	x+1x3+x+2	e)	x2+3x+1x3+2x2+1

The equation z3−3z2+4z−2=0 has the root z=1. Determine the other roots.

The equation z4+2z3+6z2+8z+8=0 has the roots z=2i and z=−1−i. Solve the equation.

Determine two real numbers a and b, such that the equation z3+az+b=0 has the root z=1−2i. Then solve the equation.

Determine a and b so that the equation \displaystyle \ z^4-6z^2+az+b=0\ has a triple root. Then solve the equation.

The equation \displaystyle \ z^4+3z^3+z^2+18z-30=0\ has a pure imaginary root. Determine all the roots.

Determine the polynomial which has the following zeros

\displaystyle 1\,, \displaystyle \,2\, and \displaystyle \,4

\displaystyle -1+ i\, and \displaystyle \,-1-i