2.3 Exercises
From Förberedande kurs i matematik 1
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|width="25%" | <math>x^2+5x+3</math> | |width="25%" | <math>x^2+5x+3</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:1|Solution a|Lösning 2.3:1a|Solution b|Lösning 2.3:1b|Solution c|Lösning 2.3:1c|Solution d|Lösning 2.3:1d}} |
===Exercise 2.3:2=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:2|Solution a|Lösning 2.3:2a|Solution b|Lösning 2.3:2b|Solution c|Lösning 2.3:2c|Solution d|Lösning 2.3:2d|Solution e|Lösning 2.3:2e|Solution f|Lösning 2.3:2f}} |
===Exercise 2.3:3=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:3|Solution a|Lösning 2.3:3a|Solution b|Lösning 2.3:3b|Solution c|Lösning 2.3:3c|Solution d|Lösning 2.3:3d|Solution e|Lösning 2.3:3e|Solution f|Lösning 2.3:3f}} |
===Exercise 2.3:4=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:4|Solution a|Lösning 2.3:4a|Solution b|Lösning 2.3:4b|Solution c|Lösning 2.3:4c}} |
===Exercise 2.3:5=== | ===Exercise 2.3:5=== | ||
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|- | |- | ||
|b) | |b) | ||
| - | |width="100" | Determine a value of <math>\,x\,</math> which makes the expression <math>\,4x^2-28x+48\,</math> | + | |width="100" | Determine a value of <math>\,x\,</math> which makes the expression <math>\,4x^2-28x+48\,</math> negative. |
|- | |- | ||
|c) | |c) | ||
|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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:5|Solution a|Lösning 2.3:5a|Solution b|Lösning 2.3:5b|Solution c|Lösning 2.3:5c}} |
===Exercise 2.3:6=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:6|Solution a|Lösning 2.3:6a|Solution b|Lösning 2.3:6b|Solution c|Lösning 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:7|Solution a|Lösning 2.3:7a|Solution b|Lösning 2.3:7b|Solution c|Lösning 2.3:7c}} |
===Exercise 2.3:8=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:8|Solution a|Lösning 2.3:8a|Solution b|Lösning 2.3:8b|Solution c|Lösning 2.3:8c}} |
===Exercise 2.3:9=== | ===Exercise 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: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:9|Solution a|Lösning 2.3:9a|Solution b|Lösning 2.3:9b|Solution c|Lösning 2.3:9c}} |
===Exercise 2.3:10=== | ===Exercise 2.3:10=== | ||
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{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="50%" | <math>y \geq x^2\ </math> | + | |width="50%" | <math>y \geq x^2\ </math> and <math>\ y \leq 1 </math> |
|b) | |b) | ||
| - | |width="50%" | <math>y \leq 1-x^2\ </math> | + | |width="50%" | <math>y \leq 1-x^2\ </math> and <math>\ x \geq 2y-3 </math> |
|- | |- | ||
|c) | |c) | ||
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|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.3:10|Solution a|Lösning 2.3:10a|Solution b|Lösning 2.3:10b|Solution c|Lösning 2.3:10c|Solution d|Lösning 2.3:10d}} |
Revision as of 14:54, 18 August 2008
| Theory | Exercises |
Exercise 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 |
Answer
Loading...
Solution a
Solution b
Solution c
Solution d
Exercise 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 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 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 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 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} |
Exercise 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\,. |
Exercise 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 |
Exercise 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 |
Exercise 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 |
Exercise 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 |
Exercise 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 |
Answer
Solution a
Solution b
Solution c
Solution d
