9.5E: Exercises

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Feb 14, 2022
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- 9.5: Solve Quadratic Equations in Quadratic Form
- 9.6: Solve Applications of Quadratic Equations

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Practice Makes Perfect

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

In the following exercises, solve.

$x^{4}-7 x^{2}+12=0$
$x^{4}-9 x^{2}+18=0$
$x^{4}-13 x^{2}-30=0$
$x^{4}+5 x^{2}-36=0$
$2 x^{4}-5 x^{2}+3=0$
$4 x^{4}-5 x^{2}+1=0$
$2 x^{4}-7 x^{2}+3=0$
$3 x^{4}-14 x^{2}+8=0$
$(x-3)^{2}-5(x-3)-36=0$
$(x+2)^{2}-3(x+2)-54=0$
$(3 y+2)^{2}+(3 y+2)-6=0$
$(5 y-1)^{2}+3(5 y-1)-28=0$
$\left(x^{2}+1\right)^{2}-5\left(x^{2}+1\right)+4=0$
$\left(x^{2}-4\right)^{2}-4\left(x^{2}-4\right)+3=0$
$2\left(x^{2}-5\right)^{2}-5\left(x^{2}-5\right)+2=0$
$2\left(x^{2}-5\right)^{2}-7\left(x^{2}-5\right)+6=0$
$x-\sqrt{x}-20=0$
$x-8 \sqrt{x}+15=0$
$x+6 \sqrt{x}-16=0$
$x+4 \sqrt{x}-21=0$
$6 x+\sqrt{x}-2=0$
$6 x+\sqrt{x}-1=0$
$10 x-17 \sqrt{x}+3=0$
$12 x+5 \sqrt{x}-3=0$
$x^{\frac{2}{3}}+9 x^{\frac{1}{3}}+8=0$
$x^{\frac{2}{3}}-3 x^{\frac{1}{3}}=28$
$x^{\frac{2}{3}}+4 x^{\frac{1}{3}}=12$
$x^{\frac{2}{3}}-11 x^{\frac{1}{3}}+30=0$
$6 x^{\frac{2}{3}}-x^{\frac{1}{3}}=12$
$3 x^{\frac{2}{3}}-10 x^{\frac{1}{3}}=8$
$8 x^{\frac{2}{3}}-43 x^{\frac{1}{3}}+15=0$
$20 x^{\frac{2}{3}}-23 x^{\frac{1}{3}}+6=0$
$x-8 x^{\frac{1}{2}}+7=0$
$2 x-7 x^{\frac{1}{2}}=15$
$6 x^{-2}+13 x^{-1}+5=0$
$15 x^{-2}-26 x^{-1}+8=0$
$8 x^{-2}-2 x^{-1}-3=0$
$15 x^{-2}-4 x^{-1}-4=0$

Answer

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

Explain how to recognize an equation in quadratic form.
Explain the procedure for solving an equation in quadratic form.

Answer: 1. Answers will vary.

Self Check

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

This table provides a checklist to evaluate mastery of the objectives of this section. Choose how would you respond to the statement â€œI can solve equations in quadratic form.â€ â€œConfidently,â€ â€œwith some help,â€ or â€œNo, I donâ€™t get it.â€ — Figure 9.4.43

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?

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

Exercise $\PageIndex{12}$ writing exercises

Practice Makes Perfect

Exercise 9.5E.11\PageIndex{11} Solve equations in quadratic form

Exercise 9.5E.12\PageIndex{12} writing exercises

Self Check

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

Exercise $\PageIndex{12}$ writing exercises