1.6e: Exercises - Quadratic in Form
- Page ID
- 45457
A: Quadratic in Form Polynomial Equations
Exercise \(\PageIndex{A} \)
\(\bigstar \) Solve quadratic in form 4th degree equations.
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- Answers to odd exercises:
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1. \(\pm 2 \sqrt{2}, \pm 3 i \)
3. \(\pm 2, \pm 3 \)
5. \(\pm \sqrt{7-\sqrt{3}}, \pm \sqrt{7+\sqrt{3}} \)
7. \(\pm 1.26, \pm 2.10 \) or \( \pm \sqrt {3 \pm \sqrt{2}} \)9. \(\pm 1.61, \pm 2.33 \) or \( \pm \sqrt {4 \pm \sqrt{2}} \)
11. \(\pm 1.06, \pm 1.69 \) or \( \pm \sqrt {2 \pm \frac{1}{2}\sqrt{3}} \)
13. \(x=\pm \sqrt{3}, x=\pm 2 \)
15. \(x=\pm \sqrt{15}, x=\pm \sqrt{2} i \)17. \(x=\pm 1, x=\frac{ \pm \sqrt{6}}{2} \)
19. \(x=\pm \sqrt{3}, x=\pm \frac{\sqrt{2}}{2} \)
21. \( \{ \pm 3, \pm \sqrt{2} \} \)
23. \( \{ \pm \frac {3}{2}. \pm \frac{\sqrt3}{3} \} \)
\(\bigstar \) Solve quadratic in form polynomial equations.
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43. \( (x^2-2x+3)^2 -5(x^2-2x+3) + 6 = 0 \) | 44. \( (x^2+x-2)^2 -5(x^2+x-2) - 50 = 0 \) |
- Answers to odd exercises
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31. \(-2,1,1 \pm i \sqrt{3},-\frac{1}{2} \pm \frac{\sqrt{3}}{2} i \)
33. \(\pm \frac{1}{3}, \pm \frac{i}{3} \)
35. \(x=12\), \(x=-1\)37. \(x=-\frac{5}{3}, x=0 \)
39. \(x=0, x=\pm \sqrt{3} \)41. \(x=\pm \sqrt{7}, x=\pm \frac{\sqrt{22}}{2} \)
43. \( \{ 0, 1, 1, 2 \} \)
B. Quadratic in Form Radical and Exponential Equations
Exercise \(\PageIndex{B} \)
\(\bigstar \) Solve quadratic in form radical equations.
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- Answers to odd exercises:
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51. \(1 \)
53. \(4,9 \)
55. \(x=25 \)57. \(x=4 \)
59. \(x=\frac{1}{4} \)61. \(x=\frac{1}{25}, x=\frac{9}{4} \)
63. \( \{ 9 \} \)65. \(x=1, x=49 \)
67. \(1, 16 \)69. \( \{ 81 \} \)
71. \(\frac{1}{64}, 1 \)
\(\bigstar \) Solve quadratic in form radical equations.
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- Answers to odd exercises:
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81. \(-27, -8 \);
83. \(\frac{1}{8} \)
85. \(-1, \frac{1}{512} \)87. \(x=8, x=-216 \)
89. \(x=\frac{27}{8}, x=-\frac{64}{27} \)
91. \(x=\frac{27}{512}, x=125 \)93. \(x=-1, x=-512 \)
95. \( \{ 216, -27 \} \)
97. \( \{ 22 \pm 10\sqrt {7} \} \)99. \( \{ \frac {8}{27},-\frac{125}{8} \} \)
101. \(0, \frac {1}{8} \)
103. \( \{ \pm 8, \pm 27 \} \)
C: Quadratic in Form Negative Exponential Equations
Exercise \(\PageIndex{C} \)
\(\bigstar \) Solve quadratic in form negative exponential equations.
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- Answers to odd exercises:
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111. \(-\frac{1}{2}, 5 \)
113. \(-\frac{2}{5}, \frac{4}{3} \)115. \(-2,1 \)
117. \(x=-10, x=\frac{1}{2} \)119. \(x=\frac{3}{4}, x=\frac{5}{2} \).
121. \( x=\frac{3}{2}, x=-\frac{5}{2} \)125. \(y = -4\)
127. \(\frac{1}{16}, 16 \)
D: Quadratic in Form Rational Equations
Exercise \(\PageIndex{D} \): Quadratic in Form Rational Equations
\(\bigstar \) Solve quadratic in form rational equations.
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- Answers to odd exercises:
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131. \(\pm \frac{3}{5} \) 133. \(-\frac{3}{2},-\frac{1}{3} \) 135. \(-\frac{3}{2}, 6 \) 137. \( \{ 15, \frac{15}{4} \} \) 139. \( \{ \pm 3, \; \pm 3i \} \) 141. \( \{ 9 \} \)