11 x1 t10 03 equations reducible to quadratics (2013)

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11 x1 t10 03 equations reducible to quadratics (2013)

  1. 1. Equations Reducible To Quadratics
  2. 2. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  
  3. 3. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x
  4. 4. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x
  5. 5. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m  
  6. 6. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  
  7. 7. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  
  8. 8. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  
  9. 9. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x  
  10. 10. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions
  11. 11. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x  
  12. 12. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   
  13. 13. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm 
  14. 14. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    
  15. 15. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m  
  16. 16. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m    3 1 0m m  
  17. 17. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m    3 1 0m m  3 or 1m m 
  18. 18. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m    3 1 0m m  3 or 1m m 3 3 or 3 1x x 
  19. 19. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m    3 1 0m m  3 or 1m m 3 3 or 3 1x x 1x 
  20. 20. Equations Reducible To Quadratics4 2e.g. ( ) 4 12 0i x x  2let m x2 4m x24 12 0m m    6 2 0m m  6 or 2m m  2 26 or 2x x  6x   no real solutions6x   ( ) 9 4 3 3 0x xii   let 3xm    22 2 23 3 3 9xx x xm    24 3 0m m    3 1 0m m  3 or 1m m 3 3 or 3 1x x 1x  or 0x 
  21. 21. Exercise 8D; 1, 2ad, 3b, 4ab, 5ac, 6a, 8abi, 9a*

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