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Name: __________________ 1 A partial solution set x 3 + 6x 2 (4) Class: Date: _____________ is given for the equation 15x 100 = 0 Find the complete solution set. 2 A partial solution set x 3 + 9x 2 ( 3) is given for the equation + 11x 21 = 0 Find the complete solution set. 3 A partial solution set x 4 4x 3 11x ( 2, 2 ) 2 is given for the equation + 60x 60 = 0 Find the complete solution set. 4 A partial solution set x 4 10x 3 ( 6,4 ) + 25x 2 is given for the equation 10x + 24 = 0 Find the complete solution set. 5 Find a polynomial with the zeros (7 , 3). 6 Find a polynomial with the zeros (6 , 5 , 1). 7 Find a polynomial with the zeros ( 8 Find a polynomial with the zeros ( 0,0,0, 2 , 9 Find a polynomial with the zeros (i, ). 10 Find a polynomial with the zeros PAGE 1 1,5, 6 , i 7, 7 ). 2 ( 0,2 i,2 + i ) ). . Name: __________________ Class: Date: _____________ 11 Use synthetic division to express P (x) = 5x 3 30x 2 32x 37 in the form (divisor)(quotient) + remainder for the divisor x 7 12 Use synthetic division to express P(x) = 5x 3 + 14x 2 22x + 28 in the form (divisor)(quotient) + remainder for the divisor 13 Use synthetic division to do the division 2x 3 2 + 3x + 18x 23 x 1 14 Use synthetic division to do the division 3x 3 2 7x 5x + 29 x + 1 15 Use synthetic division to do the division 2x 4 PAGE 2 3 2x 91x + 4 x 4 x + 4 Name: __________________ Class: 16 Use synthetic division to do the division 3x 5 7203x x 7 17 Let P(x) = 5x 3 + 2x 2 5x + 6 Use synthetic division to find the value P( 5 ) 18 Let P(x) = 3x 4 7x 2 + 5 Use synthetic division to find the value P( 5i ) 19 Let P(x) = x 4 10x 3 + 4x + 6x 2 7 Write the terms of P(x) in descending powers of x 20 Let 2 P(x) = 3 4x + 4x 5 5x 3 Use synthetic division to find the value P( 2i ) 21 Tell how many roots the equation has. 2 x =3 22 Tell how many roots the following has 15 7x PAGE 3 6x13 4x = 3 Date: _____________ Name: __________________ Class: Date: _____________ 23 Tell how many roots the equation has x104 x4 = 1 24 One root of the equation x (7x 6) = 5x 6 is 0. How many other roots are there? 25 One root of the equation 5x (x 9x + 7) = 0 2 7 is 0. How many other roots are there? 26 Write a third degree polynomial equation with real coefficients and the roots 4 , i. 27 Write a third degree polynomial equation with real coefficients and the roots 2 , i. 28 Write a third degree polynomial equation with real coefficients and the roots 3 , 3 + i. 29 Write a third degree polynomial equation with real coefficients and the roots 8 i , 1. 30 Write a fourth degree polynomial equation with real coefficients and the roots 3, 5, i. 31 Write a fourth degree polynomial equation with real coefficients and the roots 1 , 4 , 2 + i. 32 Write a fourth degree polynomial equation with real coefficients and the roots i , 1 i. 33 Find integer bounds for the roots of the equation x 2x 9 = 0 2 34 Find integer bounds for the roots of the equation 6x 13x 110x = 0 3 PAGE 4 2 Name: __________________ 35 Find integer bounds for the roots of the equation 3x 11x 2x 5 4 3 + 38x 21x 15 = 0 2 36 Find all rational roots of the equation. x 5x x + 5 = 0 2 3 37 Find all rational roots of the equation. x 3x 9x + 27 = 0 3 2 38 Find all rational roots of the equation. x + 5x x 5 = 0 3 2 39 Find all rational roots of the equation. x 13x + 56x 92x + 48 = 0 4 3 2 40 Find all rational roots of the equation. 4 3 2 x + 8x + 24x + 32x + 16 = 0 41 Find all rational roots of the equation. x 9x + 17x + 9x 18 = 0 3 4 2 42 Find all rational roots of the equation. x 2x 10x + 20x + 9x 18 = 0 5 4 3 2 43 Find all rational roots of the equation. x 48x + 768x 4096x = 0 5 7 3 44 Find all rational roots of the equation. 75x 50x + 27x 18 = 0 2 3 45 Find all rational roots of the equation. 20x + 76x 111x + 44x 5 = 0 4 3 2 46 Find all rational roots of the equation. 26x 15x + 27x 15x + 1 = 0 4 3 2 47 Find all rational roots of the equation. 7x 3x + 28x 12 = 0 3 PAGE 5 2 Class: Date: _____________ Name: __________________ Class: 48 Find all rational roots of the equation. 7x 2x + 7x 2 = 0 2 3 49 The number (1 + i) is a root of the equation. x 11x + 20x 18 = 0 3 2 Find the other roots of the equation. 50 The number (1 + i) is a root of the equation. x 2x 47x 3 4 2 + 98x 98 = 0 Find the other roots of the equation. 51 The number (1 + i) is a root of the equation. x 2x 47x 3 4 2 + 98x 98 = 0 Find the other roots of the equation. 52 The number (1 + i) is a root of the equation. x 2x 79x + 162x 162 = 0 4 3 2 Find the other roots of the equation. 53 Solve the equation. x 3 32 x 2 + 92 x 16 = 0 3 3 54 Find all rational roots of the equation. 1 1 5x 10x 2 + 50x 3 + 9x 4 45x 5 = 0 55 Find all rational roots of the equation. 1 1 16x 2 + 91x 216x 3 + 180x 4 = 0 56 Find the positive root of the equation using the bisection method. x 2 3 = 0 57 Find the negative root of the equation using the bisection method. x 2 2 = 0 58 Find the positive root of the equation using the bisection method. x 2 13 = 0 PAGE 6 Date: _____________ Name: __________________ Class: Date: _____________ 59 Find the negative root of the equation using the bisection method. x 2 10 = 0 60 Find the positive root of the equation using the bisection method. x 3 x 2 3 = 0 61 Find the negative root of the equation using the bisection method. x 3 x + 3 = 0 , 62 Find the negative root of the equation using the bisection method. 3x 4 + 3x 3 x 2 4x 5 = 0 , 63 Find the positive root of the equation using the bisection method. x 5 + x 4 4x 3 4x 2 5x 5 = 0 64 Use a graphing calculator to find the distinct real solutions of the equation. x 2 5 = 0 65 Use a graphing calculator to find the real solution of the equation. x 2 2x + 1 = 0 66 Use a graphing calculator to find the distinct real solutions of the equation. x 3 7x 2 + 15x 9 = 0 67 Use a graphing calculator to find the real solutions of the equation. x 3 3x PAGE 7 2 8x + 24 = 0 Name: __________________ 68 Class: Date: _____________ 3 Use the bisection method or a graphing calculator to find the coordinates of the two points on the graph of y = x that lie r = 1 unit from the origin. Give the result to the nearest hundredth. 69 The length of the shipping crate is to be 2 feet greater than its height and 5 feet greater than its width, and its volume is to be 170 cubic feet. Use the bisection method or a graphing calculator to find the height of the crate to the nearest tenth of a foot. PAGE 8 ANSWER KEY Name: __________________ Class: Date: _____________ 1. 4, 5, 5 24. 6 47. 2. 1, 3, 7 25. 8 48. 3. 2,2, 15, 26. x3 4x2+x 4=0 49. 4. 6,4, i,i 27. x3 2x2+x 2=0 50. 5. x 10x+21 28. x3 9x2+28x 30=0 51. 6. x 12x +41x 30 29. x3 15x2+49x+65=0 52. 7. x 4x 12x +28x+35 30. x4 8x3+16x2 8x+15=0 53. 8. x 2x 9. x 15 2 3 2 4 3 5 3 3 2 4 2 6 x +x 6 10. x3 4x2+5x 3 3 7 2 7 9,1 i 7, 7,1 i 7,1 i 7, 7,1 i,1+i 7, 7,1 i 7,1 i,1+i 7,1 i 7, 7,1 i 7,1 i 7, 7,1 i,1+i 7, 7,1 i 7,1 i,1+i 7,1 i 9, 9,1 i 2 ,6,4 3 2 31. x 9x +29x 41x+20=0 54. 1,3, 1, 3,5 32. x4 2x3+3x2 2x+2=0 55. 2,5,3,6 33. 2,5 56. 1.7 x=1.7 1.4 x= 1.4 11. ( x 7) ( 5x +5x+3) 16 2 ( x 7) ( 5x +5x+3) 16 34. 4,6 57. 12. ( x+4 ) ( 5x 6x+2 ) +20 35. 2,4 58. 36. 1, 1,5 59. 37. 3, 3,3 60. 38. 1, 1, 5 61. 16. 3x +21x +147x +1029x 39. 2,4,1,6 62. 17. 656 40. 2, 2, 2, 2 63. 18. 2055 41. 1,6, 1,3 64. 19. x4 10x3+6x2+4x 7 42. 1,3, 1, 3,2 65. 20. 19+168i 43. 0,4,4,4, 4, 4, 4 66. 21. 2 2 44. 3 67. 2.8, 2.8,3.0 2 2 13. 2x2+5x+23 2 14. 3x 10x+5+ 3 24 x+1 2 15. 2x +6x +24x+5+ 4 PAGE 1 3 24 x 4 2 3.6 x=3.6 3.2 x= 3.2 1.9 x=1.9 1.7 x= 1.7 1.3 x= 1.3 2.2 x=2.2 2.2, 2.2 1 x=1 1,3 ANSWER KEY Name: __________________ 22. 15 23. 104 PAGE 2 Class: 1 , 1 , 5, 1 2 2 5 1, 1 46. 2 13 45. Date: _____________ 68. ( 0.83,0.56 ) , ( 0.83, 0.56 ) 69. 6.3