Processing Math: Done

To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.

jsMath

Warning: jsMath requires JavaScript to process the mathematics on this page.
If your browser supports JavaScript, be sure it is enabled.

3.4 Übungen

(Unterschied zwischen Versionen)

Version vom 13:44, 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 z4−6z2+az+b=0 has a triple root. Then solve the equation.

The equation z4+3z3+z2+18z−30=0 has a pure imaginary root. Determine all the roots.

Determine the polynomial which has the following zeros

1, 2 and 4

−1+i and −1−i