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Equations Reducible To Quadratics
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11X1 T11 03 equations reducible to quadratics

Jun 29, 2015

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Nigel Simmons
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Page 1: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics

Page 2: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

Page 3: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x

Page 4: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

Page 5: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m

Page 6: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

Page 7: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m

Page 8: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

Page 9: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x

Page 10: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

Page 11: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

Page 12: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

Page 13: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm

Page 14: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm

Page 15: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

Page 16: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

3 1 0m m

Page 17: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

3 1 0m m

3 or 1m m

Page 18: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

3 1 0m m

3 or 1m m

3 3 or 3 1x x

Page 19: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

3 1 0m m

3 or 1m m

3 3 or 3 1x x 1x

Page 20: 11X1 T11 03 equations reducible to quadratics

Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x

2let m x2 4m x

2 4 12 0m m 6 2 0m m

6 or 2m m 2 26 or 2x x

6x no real solutions

6x

( ) 9 4 3 3 0x xii

let 3xm 22 2 23 3 3 9

xx x xm 2 4 3 0m m

3 1 0m m

3 or 1m m

3 3 or 3 1x x 1x or 0x

Page 21: 11X1 T11 03 equations reducible to quadratics

Exercise 8D; 1, 2ad, 3b, 4ab, 5ac, 6a, 8abi, 9a*