3.4 Übungen
Aus Online Mathematik Brückenkurs 2
| Theory |
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Exercise 3.4:1
Carry out the following divisions (not all are exact, i.e. have no remainder)
| a) | \displaystyle \displaystyle\frac{x^2-1}{x-1} | b) | \displaystyle \displaystyle\frac{x^2}{x+1} | c) | \displaystyle \displaystyle \frac{x^3+a^3}{x+a} |
| d) | \displaystyle \displaystyle\frac{x^3 +x+2}{x+1} | e) | \displaystyle \displaystyle \frac{x^3+2x^2+1}{x^2+3x+1} |
Laden...Exercise 3.4:2
The equation \displaystyle \,z^3-3z^2+4z-2=0\, has the root \displaystyle \,z=1\,. Determine the other roots.
Exercise 3.4:3
The equation \displaystyle \,z^4+2z^3+6z^2 +8z +8 =0\, has the roots \displaystyle \,z=2i\, and \displaystyle \,z=-1-i\,. Solve the equation.
Exercise 3.4:4
Determine two real numbers \displaystyle \,a\, and \displaystyle \,b\,, such that the equation \displaystyle \ z^3+az+b=0\ has the root \displaystyle \,z=1-2i\,. Then solve the equation.
Exercise 3.4:5
Determine \displaystyle \,a\, and \displaystyle \,b\, so that the equation \displaystyle \ z^4-6z^2+az+b=0\ has a triple root. Then solve the equation.
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.
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 |
