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# 9.5E: Exercises

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### Practice Makes Perfect

##### Exercise $$\PageIndex{11}$$ Solve equations in quadratic form

In the following exercises, solve.

1. $$x^{4}-7 x^{2}+12=0$$
2. $$x^{4}-9 x^{2}+18=0$$
3. $$x^{4}-13 x^{2}-30=0$$
4. $$x^{4}+5 x^{2}-36=0$$
5. $$2 x^{4}-5 x^{2}+3=0$$
6. $$4 x^{4}-5 x^{2}+1=0$$
7. $$2 x^{4}-7 x^{2}+3=0$$
8. $$3 x^{4}-14 x^{2}+8=0$$
9. $$(x-3)^{2}-5(x-3)-36=0$$
10. $$(x+2)^{2}-3(x+2)-54=0$$
11. $$(3 y+2)^{2}+(3 y+2)-6=0$$
12. $$(5 y-1)^{2}+3(5 y-1)-28=0$$
13. $$\left(x^{2}+1\right)^{2}-5\left(x^{2}+1\right)+4=0$$
14. $$\left(x^{2}-4\right)^{2}-4\left(x^{2}-4\right)+3=0$$
15. $$2\left(x^{2}-5\right)^{2}-5\left(x^{2}-5\right)+2=0$$
16. $$2\left(x^{2}-5\right)^{2}-7\left(x^{2}-5\right)+6=0$$
17. $$x-\sqrt{x}-20=0$$
18. $$x-8 \sqrt{x}+15=0$$
19. $$x+6 \sqrt{x}-16=0$$
20. $$x+4 \sqrt{x}-21=0$$
21. $$6 x+\sqrt{x}-2=0$$
22. $$6 x+\sqrt{x}-1=0$$
23. $$10 x-17 \sqrt{x}+3=0$$
24. $$12 x+5 \sqrt{x}-3=0$$
25. $$x^{\frac{2}{3}}+9 x^{\frac{1}{3}}+8=0$$
26. $$x^{\frac{2}{3}}-3 x^{\frac{1}{3}}=28$$
27. $$x^{\frac{2}{3}}+4 x^{\frac{1}{3}}=12$$
28. $$x^{\frac{2}{3}}-11 x^{\frac{1}{3}}+30=0$$
29. $$6 x^{\frac{2}{3}}-x^{\frac{1}{3}}=12$$
30. $$3 x^{\frac{2}{3}}-10 x^{\frac{1}{3}}=8$$
31. $$8 x^{\frac{2}{3}}-43 x^{\frac{1}{3}}+15=0$$
32. $$20 x^{\frac{2}{3}}-23 x^{\frac{1}{3}}+6=0$$
33. $$x-8 x^{\frac{1}{2}}+7=0$$
34. $$2 x-7 x^{\frac{1}{2}}=15$$
35. $$6 x^{-2}+13 x^{-1}+5=0$$
36. $$15 x^{-2}-26 x^{-1}+8=0$$
37. $$8 x^{-2}-2 x^{-1}-3=0$$
38. $$15 x^{-2}-4 x^{-1}-4=0$$

1. $$x=\pm \sqrt{3}, x=\pm 2$$

3. $$x=\pm \sqrt{15}, x=\pm \sqrt{2} i$$

5. $$x=\pm 1, x=\frac{ \pm \sqrt{6}}{2}$$

7. $$x=\pm \sqrt{3}, x=\pm \frac{\sqrt{2}}{2}$$

9. $$x=-1, x=12$$

11. $$x=-\frac{5}{3}, x=0$$

13. $$x=0, x=\pm \sqrt{3}$$

15. $$x=\pm \frac{11}{2}, x=\pm \frac{\sqrt{22}}{2}$$

17. $$x=25$$

19. $$x=4$$

21. $$x=\frac{1}{4}$$

23. $$x=\frac{1}{25}, x=\frac{9}{4}$$

25. $$x=-1, x=-512$$

27. $$x=8, x=-216$$

29. $$x=\frac{27}{8}, x=-\frac{64}{27}$$

31. $$x=27, x=64,000$$

33. $$x=1, x=49$$

35. $$x=-2, x=-\frac{3}{5}$$

37. $$x=-2, x=\frac{4}{3}$$

##### Exercise $$\PageIndex{12}$$ writing exercises
1. Explain how to recognize an equation in quadratic form.
2. Explain the procedure for solving an equation in quadratic form.

## Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

9.5E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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