11X1 T10 07 sum & product of roots (2011)

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<ul><li>1.Sum and Product of Roots</li></ul> <p>2. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; 3. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x 4. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x ax 2 bx c a x 2 x x 5. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x ax 2 bx c a x 2 x x b c x 2 x x 2 x a a 6. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x ax 2 bx c a x 2 x x b c x 2 x x 2 x a a Thus 7. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x ax 2 bx c a x 2 x x b c x 2 x x 2 x a a Thusb (sum of roots)a 8. Sum and Product of Roots If and are the roots of ax 2 bx c 0, then; ax 2 bx c a x x ax 2 bx c a x 2 x x b c x 2 x x 2 x a a Thusb (sum of roots)ac (product of roots)a 9. e.g. (i) Form a quadratic equation whose roots are; 10. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 11. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 1 12. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 1 6 13. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 1 6x2 x 6 0 14. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 6x2 x 6 0 15. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6x2 x 6 0 16. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1 17. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 18. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 (ii ) If and are the roots of 2x 2 3 x 1 0, find; 19. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 (ii ) If and are the roots of 2x 2 3 x 1 0, find;a) 20. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 (ii ) If and are the roots of 2x 2 3 x 1 0, find; ba) a 3 2 21. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 (ii ) If and are the roots of 2x 2 3 x 1 0, find; bb) a) a 3 2 22. e.g. (i) Form a quadratic equation whose roots are;a ) 2 and 3 b) 2 5 and 2 5 1 4 6 4 5x2 x 6 0 1x2 4x 1 0 (ii ) If and are the roots of 2x 2 3 x 1 0, find; bb) ca) a a 31 2 2 23. c) 2 2 24. c) 2 2 2 2 25. c) 2 2 2212 2 3 2 2 26. c) 2 2 2212 2 3 2 29 1413 4 27. 1 1c) 22 2 2d) 12 2 3 2 29 1413 4 28. 1 1 c) 2 d) 2 2 2 12 2 3 2 29 1413 4 29. 1 1 c) 2 d) 2 2 2 12 2 3 3 2 2 29 1 12413 4 30. 1 1 c) 2 d) 2 22 1 23 3 2 2 2 29 1 12413 3 4 31. 1 1 c) 2d) 222 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0 32. 1 1 c) 2d) 222 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 33. 1 1 c) 2d) 222 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 34. 1 1 c) 2d) 22 2 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 3 6 2 35. 1 1 c) 2d) 22 2 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 2 m 3 6 2 36. 1 1 c) 2d) 22 2 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 2 m3 62 2 m 2 37. 1 1 c) 2d) 222 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 2 m3 6 2 2 m2 2 m2 2 38. 1 1 c) 2d) 222 12 2 3 3 2 2 2 9 1 12 4 13 3 4(iii ) Find the value of m if one root is double the other in x 2 6 x m 0Let the roots be and 2 2 6 2 m3 6 2 2 m2 2 m2 2 m8 39. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 40. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 1Let the roots be and 41. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 1Let the roots be and 1 1 2m 1 42. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 1Let the roots be and 1 1 2m 11 12m 1 43. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 1Let the roots be and 1 1 2m 11 12m 1 2m 1 1 2m 2m 1 44. (iv) Find the values of m in 2m 1 x 2 1 m x 1 0, if one root is the reciprocal of the other. 1Let the roots be and 1 1 2m 11 12m 1 2m 1 1 2m 2m 1 Exercise 8H; 3beh, 4bdf, 5, 6, 7abc i, 8, 10, 12,13cd, 15, 18, 20, 21ac </p>