2.3 Übungen
Aus Online Mathematik Brückenkurs 1
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|width="25%" | <math>x^2+5x+3</math> | |width="25%" | <math>x^2+5x+3</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:1| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:1|Lösung a|Lösung 2.3:1a|Lösung b|Lösung 2.3:1b|Lösung c|Lösung 2.3:1c|Lösung d|Lösung 2.3:1d}} |
===Übung 2.3:2=== | ===Übung 2.3:2=== | ||
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|width="33%" | <math>3x^2-10x+8=0</math> | |width="33%" | <math>3x^2-10x+8=0</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:2| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:2|Lösung a|Lösung 2.3:2a|Lösung b|Lösung 2.3:2b|Lösung c|Lösung 2.3:2c|Lösung d|Lösung 2.3:2d|Lösung e|Lösung 2.3:2e|Lösung f|Lösung 2.3:2f}} |
===Übung 2.3:3=== | ===Übung 2.3:3=== | ||
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|width="50%" | <math>x(x^2-2x)+x(2-x)=0</math> | |width="50%" | <math>x(x^2-2x)+x(2-x)=0</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:3| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:3|Lösung a|Lösung 2.3:3a|Lösung b|Lösung 2.3:3b|Lösung c|Lösung 2.3:3c|Lösung d|Lösung 2.3:3d|Lösung e|Lösung 2.3:3e|Lösung f|Lösung 2.3:3f}} |
===Übung 2.3:4=== | ===Übung 2.3:4=== | ||
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|width="100" | <math>3\ </math> and <math>\ \sqrt{3}</math> | |width="100" | <math>3\ </math> and <math>\ \sqrt{3}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:4| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:4|Lösung a|Lösung 2.3:4a|Lösung b|Lösung 2.3:4b|Lösung c|Lösung 2.3:4c}} |
===Übung 2.3:5=== | ===Übung 2.3:5=== | ||
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|width="100" | The equation <math>\,x^2+4x+b=0\,</math> has one root at <math>\,x=1\,</math>. Determine the value of the constant <math>\,b\,</math>. | |width="100" | The equation <math>\,x^2+4x+b=0\,</math> has one root at <math>\,x=1\,</math>. Determine the value of the constant <math>\,b\,</math>. | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:5| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:5|Lösung a|Lösung 2.3:5a|Lösung b|Lösung 2.3:5b|Lösung c|Lösung 2.3:5c}} |
===Übung 2.3:6=== | ===Übung 2.3:6=== | ||
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|width="33%" | <math>x^2-5x+7</math> | |width="33%" | <math>x^2-5x+7</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:6| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:6|Lösung a|Lösung 2.3:6a|Lösung b|Lösung 2.3:6b|Lösung c|Lösung 2.3:6c}} |
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|width="33%" | <math>x^2+x+1</math> | |width="33%" | <math>x^2+x+1</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:7| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:7|Lösung a|Lösung 2.3:7a|Lösung b|Lösung 2.3:7b|Lösung c|Lösung 2.3:7c}} |
===Übung 2.3:8=== | ===Übung 2.3:8=== | ||
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|width="33%" | <math>f(x)=x^2-6x+11</math> | |width="33%" | <math>f(x)=x^2-6x+11</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:8| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:8|Lösung a|Lösung 2.3:8a|Lösung b|Lösung 2.3:8b|Lösung c|Lösung 2.3:8c}} |
===Übung 2.3:9=== | ===Übung 2.3:9=== | ||
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|width="33%" | <math>y=3x^2-12x+9</math> | |width="33%" | <math>y=3x^2-12x+9</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:9| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:9|Lösung a|Lösung 2.3:9a|Lösung b|Lösung 2.3:9b|Lösung c|Lösung 2.3:9c}} |
===Übung 2.3:10=== | ===Übung 2.3:10=== | ||
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|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:10| | + | </div>{{#NAVCONTENT:Antwort|Antwort 2.3:10|Lösung a|Lösung 2.3:10a|Lösung b|Lösung 2.3:10b|Lösung c|Lösung 2.3:10c|Lösung d|Lösung 2.3:10d}} |
Version vom 09:29, 22. Okt. 2008
Übung 2.3:1
Complete the square of the expressions
| a) | \displaystyle x^2-2x | b) | \displaystyle x^2+2x-1 | c) | \displaystyle 5+2x-x^2 | d) | \displaystyle x^2+5x+3 |
Antwort
Laden...
Lösung a
Lösung b
Lösung c
Lösung d
Übung 2.3:2
Solve the following second order equations by completing the square
| a) | \displaystyle x^2-4x+3=0 | b) | \displaystyle y^2+2y-15=0 | c) | \displaystyle y^2+3y+4=0 |
| d) | \displaystyle 4x^2-28x+13=0 | e) | \displaystyle 5x^2+2x-3=0 | f) | \displaystyle 3x^2-10x+8=0 |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Übung 2.3:3
Solve the following equations directly
| a) | \displaystyle x(x+3)=0 | b) | \displaystyle (x-3)(x+5)=0 |
| c) | \displaystyle 5(3x-2)(x+8)=0 | d) | \displaystyle x(x+3)-x(2x-9)=0 |
| e) | \displaystyle (x+3)(x-1)-(x+3)(2x-9)=0 | f) | \displaystyle x(x^2-2x)+x(2-x)=0 |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Übung 2.3:4
Determine a second-degree equation which has roots
| a) | \displaystyle -1\ and \displaystyle \ 2 |
| b) | \displaystyle 1+\sqrt{3}\ and \displaystyle \ 1-\sqrt{3} |
| c) | \displaystyle 3\ and \displaystyle \ \sqrt{3} |
Übung 2.3:5
| a) | Determine a second-degree equation which only has \displaystyle \,-7\, as a root. |
| b) | Determine a value of \displaystyle \,x\, which makes the expression \displaystyle \,4x^2-28x+48\, negative. |
| c) | The equation \displaystyle \,x^2+4x+b=0\, has one root at \displaystyle \,x=1\,. Determine the value of the constant \displaystyle \,b\,. |
Übung 2.3:6
Determine the smallest value that the following polynomial can take
| a) | \displaystyle x^2-2x+1 | b) | \displaystyle x^2-4x+2 | c) | \displaystyle x^2-5x+7 |
Übung 2.3:7
Determine the largest value that the following polynomials can take.
| a) | \displaystyle 1-x^2 | b) | \displaystyle -x^2+3x-4 | c) | \displaystyle x^2+x+1 |
Übung 2.3:8
Sketch the graph of the following functions
| a) | \displaystyle f(x)=x^2+1 | b) | \displaystyle f(x)=(x-1)^2+2 | c) | \displaystyle f(x)=x^2-6x+11 |
Übung 2.3:9
Find all the points where the x-axis and the following curves intersect.
| a) | \displaystyle y=x^2-1 | b) | \displaystyle y=x^2-5x+6 | c) | \displaystyle y=3x^2-12x+9 |
Übung 2.3:10
In the xy-plane, draw in all the points whose coordinates \displaystyle \,(x,y)\, satisfy
| a) | \displaystyle y \geq x^2\ and \displaystyle \ y \leq 1 | b) | \displaystyle y \leq 1-x^2\ and \displaystyle \ x \geq 2y-3 |
| c) | \displaystyle 1 \geq x \geq y^2 | d) | \displaystyle x^2 \leq y \leq x |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
