11X1 T16 06 roots & coefficients

Download 11X1 T16 06 roots & coefficients

Post on 29-Jun-2015

413 views

Category:

Education

0 download

Embed Size (px)

TRANSCRIPT

<ul><li> 1. Roots and Coefficients </li></ul> <p> 2. Roots and CoefficientsQuadratics ax 2 bx c 0 3. Roots and CoefficientsQuadratics ax 2 bx c 0 b a 4. Roots and CoefficientsQuadratics ax 2 bx c 0 bc aa 5. Roots and CoefficientsQuadraticsax 2 bx c 0bc aaCubicsax 3 bx 2 cx d 0 6. Roots and CoefficientsQuadraticsax 2 bx c 0bc aaCubicsax 3 bx 2 cx d 0b a 7. Roots and CoefficientsQuadraticsax 2 bx c 0bc aaCubicsax 3 bx 2 cx d 0bc aa 8. Roots and CoefficientsQuadraticsax 2 bx c 0bc aaCubicsax 3 bx 2 cx d 0bc aad a 9. Roots and Coefficients Quadraticsax 2 bx c 0bc aa Cubics ax 3 bx 2 cx d 0 bc aad aQuartics ax 4 bx 3 cx 2 dx e 0 10. Roots and Coefficients Quadraticsax 2 bx c 0bc aa Cubics ax 3 bx 2 cx d 0 bc aad aQuartics ax 4 bx 3 cx 2 dx e 0b a 11. Roots and Coefficients Quadraticsax 2 bx c 0bc aa Cubics ax 3 bx 2 cx d 0 bc aad aQuartics ax 4 bx 3 cx 2 dx e 0b c a a 12. Roots and CoefficientsQuadratics ax 2 bx c 0bc aa Cubics ax 3 bx 2 cx d 0b c a ad aQuartics ax 4 bx 3 cx 2 dx e 0bc aa d a 13. Roots and CoefficientsQuadratics ax 2 bx c 0bc aa Cubics ax 3 bx 2 cx d 0b c a ad aQuartics ax 4 bx 3 cx 2 dx e 0bc aa de a a 14. For the polynomial equation; ax n bx n1 cx n2 dx n3 0 15. For the polynomial equation; ax n bx n1 cx n2 dx n3 0 b a (sum of roots, one at a time) 16. For the polynomial equation; ax n bx n1 cx n2 dx n3 0 b a(sum of roots, one at a time) c a (sum of roots, two at a time) 17. For the polynomial equation; ax n bx n1 cx n2 dx n3 0b a (sum of roots, one at a time)c a (sum of roots, two at a time)d a (sum of roots, three at a time) 18. For the polynomial equation; ax n bx n1 cx n2 dx n3 0 b a (sum of roots, one at a time) c a (sum of roots, two at a time) d a(sum of roots, three at a time)e a(sum of roots, four at a time) 19. For the polynomial equation; ax n bx n1 cx n2 dx n3 0 b a(sum of roots, one at a time) c a(sum of roots, two at a time) d a(sum of roots, three at a time)e a(sum of roots, four at a time)Note: 2 22 20. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7 21. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 2 22. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 2 2 23. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 2 24. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 2 5 14 4 4 7 4 7 2 2 25. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7531 222 5 14 4 4 7 4 7 2 2 27 2 26. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7531 2225 1 4 4 4 7 4 7 2 227 21 1 1 b) 27. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7531 2225 1 4 4 4 7 4 7 2 227 21 1 1 b) 28. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7531 2225 1 4 4 4 7 4 7 2 227 21 1 1 b) 3 2 1 2 29. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 7531 2225 1 4 4 4 7 4 7 2 227 21 1 1 b) 3 212 3 30. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 25 1 4 4 4 7 4 7 2 227 21 1 1 b) c) 2 2 2 3 212 3 31. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 25 1 4 4 4 7 4 7 2 2 27 21 1 1 b) c) 2 2 2 2 23 2 1 2 3 32. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 25 1 4 4 4 7 4 7 2 2 27 21 1 1 b) c) 2 2 2 2 23 2 5 3 2 2 1 2 2 2 3 33. e.g. (i ) If , and are the roots of 2 x 3 5 x 2 3 x 1 0, find thevalues of;a) 4 4 4 75 3 1 2 2 25 1 4 4 4 7 4 7 2 2 27 21 1 1 b) c) 2 2 2 2 23 2 5 3 2 2 1 2 2 37 2 3 4 34. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 35. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0 36. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 37. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 1 38. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 1 1 1 1 (iii) 39. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 1 1 1 1 (iii) 1 1 1 40. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 1 1 1 1 (iii) 1 1 1 31 41. 1988 Extension 1 HSC Q2c) If , and are the roots of x 3 x 1 0 find:3 (i) 0(ii) 1 1 1 1 (iii) 1 1 1 313 42. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 43. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 44. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 2 45. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 2 3 46. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 P 3 0 2 3 47. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 P 3 0 2 32 3 3 k 3 6 0 32 48. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 P 3 0 2 32 3 3 k 3 6 0 32 54 9 3k 6 0 49. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 P 3 0 2 32 3 3 k 3 6 0 32 54 9 3k 6 03k 39 50. 2003 Extension 1 HSC Q4c) It is known that two of the roots of the equation 2 x 3 x 2 kx 6 0 are reciprocals of each other. Find the value of k. 1 Let the roots be , and 1 6 P 3 0 2 32 3 3 k 3 6 0 32 54 9 3k 6 03k 39k 13 51. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r 52. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 r 53. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1 54. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t 55. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t1 1 s 56. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t1 1 ss 2 57. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t1 1 s1 ts 2 58. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t1 1 s1 ts 2t 2 59. 2006 Extension 1 HSC Q4a) The cubic polynomial P x x 3 rx 2 sx t , where r, s and t are real numbers, has three real zeros, 1, and (i) Find the value of r1 rr 1(ii) Find the value of s + t1 1 s 1 ts 2 t 2s t 0 60. Exercise 4F; 2, 4, 5ac, 6ac, 8, 10a, 13, 15,16ad, 17, 18, 19 </p>