Download Equations with Quadr..

Equations with Quadratics
Solve each of the following equations. Some equations will have complex roots.
1. x4 – 5x2 + 4 = 0
2. y4 – 9y2 + 20 = 0
3. m4 – 7m2 – 8 = 0
4. y4 – 29y2 + 100 = 0
5. a4 – 50a2 + 49 = 0
6. b4 – 10b2 + 9 = 0
7. x4 – 25x2 + 144 = 0
8. y4 – 40y2 + 144 = 0
9. m4 – 20m2 + 64 = 0
10. x6 – 35x3 + 216 = 0
11. z6 – 216 = 19z3
12. y4 – 2y2 = 24
13. 6z4 – z2 = 12
14. x–2 – x–1 – 12 = 0
2
1
15. x3 – 35 = 2x3
16. 5y–2 – 20 = 21y–1
17. y–6 + 7y–3 = 8
18. x4 – 7x2 + 12 = 0
19. x4 – 2x2 – 3 = 0
20. x4 + 7x2 + 10 = 0
21. 2x4 – 5x2 + 2 = 0
22. 2x4 – x2 – 3 = 0
23. x4 – 9x2 + 8 = 0
24. x6 – 10x3 + 16 = 0
25. 8x6 – 9x3 + 1 = 0
26. 8x6 + 7x3 – 1 = 0
27. x8 – 17x4 + 16 = 0
28. (x –1)2 – 4(x – 1) = 5
29. (y + b)2 – 4(y + b) = 21
30. (x + 1)2 + 6(x + 1) + 9 = 0
31. (y + 2)2 – 6(y + 2) = 16
32. (m – 1)2 – 5(m – 1) = 14
33. (x – 3)2 – 2(x – 3) = 35
34. (a + 1)2 + 2(a + 1) = 15
35. (r – 1)2 – 8(r – 1) = 20
36. 2(x – 1)2 – (x – 1) = 3
37. 3(y + 1)2 – 14(y + 1) = 5
38. (x2 – 3)2 – 2(x2 – 3) = 3
39. (3x2 – 2x)2 + 5 = 6(3x2 – 2x)
40. (x2 + x + 3)2 + 15 = 8(x2 + x + 3)
2
3
1
3
41. 2(3x + 1) – 5(3x + 1) = 88
42. (x2 + x)2 – 8(x2 + x) + 12 = 0
43. (x2 + 2x)2 – 2(x2 + 2x) = 3
44. (2x2 + 3x)2 = 8(2x2 + 3x) + 9
45. (2x2 – x)2 – 4(2x2 – x) + 3 = 0
46. (3x2 – 4x)2 = 3(3x2 – 4x) + 4
47. (y – 2)6 – 19(y – 2)3 = 216
48. x – x – 30 = 0
49. 5x + 12 = 5 5x + 12
50. x2 – 7 x2 – 4x + 11 = 4x – 23
51.
m2 + 3m – 3 = m2 + 3m – 23
53. c2 – 8c +
55.
c2 – 8c + 16 + 14 = 0
x2 + 3 – 5x2 – 9 = 0
57. x2 + 2x + 3 – 2 x2 + 2x + 6 = 0
52. 2r2 + 4r –
r2 + 2r – 3 = 9
54. x2 – 3x – 2 x2 – 3x + 7 = 8
56. 2y2 – y +
2y2 – y – 3 = 5
58. 3x2 + x + 5 3x2 + x –1 = 25
59.
5
12
2x + 1 + (2x + 1)2 = 3
6 2
22

60. y – y  – 4y + y = 5


 x2 – 8 2
 x2 – 8 
61.  2x  – 4 2x  + 3 = 0 62.




x2 + 12
56x
+
= 15
2
x
x + 12
 x2 + 8 2
 x2 + 8 
 x2 – 36 2
 x2 – 36 






 = 45
63.
– 11
+ 18 = 0 64.
– 4
x
x
 x 
 x 




65.
x
x–1 – 6
x
x–1
= 40
66.
2x + 1
– 30 = 7
x
2x + 1
x
 x + 22
x+2
67. 5  x – 2  = 3  x – 2  + 2




 x + 1 2
x+1
68.  x + 3  +  x + 3  = 6




 x2 + 12 2
 x2 + 12 
 – 
 = 56
69. 
x
x




 x + 8 2
x+8
70.  x – 8  – 6 = 5 x – 8 




2
2
 x2 – 40 
 x2 – 40 
 – 9
 + 18 = 40
71. 
x
x




2
 x2 – 3 
 x2 – 3 
73. 2 x  + 5 x  + 2 = 0




 x2 – 45 
 x2 – 45 
 – 8
 = 48
72. 
x
x




2
 x2 – 8 
 x2 – 8 
74.  x  – 9 x  + 14 = 0




2
2
 x2 – 18 
 x2 – 18 
 – 7
+3=0
75. 2
x
x




77.
x–3 –
1
79. x2 +
1
1
2
x
4
x–3 =2
83.
x2 + 3x + 1 = 8
x2 – x + 2
x2 + x + 2
5
+
= 2
2
2
x +x+2
x –x+2
rev 10/03/07
78. (x2 – 5x – 2)2 – 5(x2 – 5x – 2) + 4 = 0
2 2
6

80. y + y  + 3y + y = 4


13
= 6
81. x2 + 3x + 1 –
 x2 – 20 
 x2 – 20 
 + 9
+8=0
76. 
x
x




82.
2x + 1
=3+7
x
2x + 1
x
84.
2x2 – 4x + 6
9x2 – 27x + 18
+
= 9
x2 – 3x + 2
x2 – 2x + 3
Answers
i, 2 2
1.
1, 2
7.
3, 4
13.
2i 3  6
3 , 2
17.
1, – 2 ,
23.
1, 2 2
25.
1, 2,
29.
–(b + 3), 7 – b
31.
–4, 6
35.
–1, 11
37.
41.
511
3 ,
47.
0, 5, 3 i 3 ,
53.
3, 5
1
3.
9.
2, 4
1339
– 24
7
6
59.
1, –
62.
2, 3, 4, 6
1 3i 3
3
11.
–2, 3, 1  i 3,
i ,  3
19.
21.
–1 i 3 –1 i 3
,
27.
4
2
1
–3  3i 3
2
2
 2,  2
1, i , ±2, ±2i
33.
–2, 10
4, – 3
39.
1, – 3 , 3
43.
1, –3
45.
1, – 2 , 2
49.
– 5 , 5
51.
–7, 4
55.
no solution
57.
1, –3
60.
–1, –3, 2, 6
61.
–2, 4, 3  17
63.
–2, 1, 4, 8
64.
–3, –9, 4, 12
66.
1
98
67.
– 7
69.
–3, –4, 2, 8
70.
0, 5
–2, 1.5, –3, 1
–5, 4, –10, 2
4
12
13
68.
100
99
5
7
– 2,– 2
71.
74.
–4, 10, –5, 8
–1, 8, –2, 4
72.
75.
–3, 15, –9, 5
9
–3, 6, –4, 2
73.
76.
77.
19
79.
4 9
9, 4
81.
83.
1, 2
65.
1, 7
–125, 343
15.
1 i 3 –1 i 3
4 ,
2
5.
1
5
1
3
6
56
–3 
39  33
2