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3.4 Übungen

Aus Online Mathematik Brückenkurs 2

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Exercise 3.4:1

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

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 3.4:2

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

Answer | Solution

Exercise 3.4:3

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

Answer | Solution

Exercise 3.4:4

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.

Answer | Solution

Exercise 3.4:5

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

Answer | Solution

Exercise 3.4:6

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

Answer | Solution

Exercise 3.4:7

Determine the polynomial which has the following zeros

a) \displaystyle 1\,, \displaystyle \,2\, and \displaystyle \,4 b) \displaystyle -1+ i\, and \displaystyle \,-1-i

Answer | Solution a | Solution b

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/3.4_%C3%9Cbungen“