Solutions
Solutions to Try Its
1. [latex]f\left(-3\right)=-412\\[/latex] 2. The zeros are 2, –2, and –4. 3. There are no rational zeros. 4. The zeros are [latex]\text{-4, }\frac{1}{2},\text{ and 1}\text{.}\\[/latex] 5. [latex]f\left(x\right)=-\frac{1}{2}{x}^{3}+\frac{5}{2}{x}^{2}-2x+10\\[/latex] 6. There must be 4, 2, or 0 positive real roots and 0 negative real roots. The graph shows that there are 2 positive real zeros and 0 negative real zeros. 7. 3 meters by 4 meters by 7 metersSolutions to Odd-Numbered Exercises
1. The theorem can be used to evaluate a polynomial. 3. Rational zeros can be expressed as fractions whereas real zeros include irrational numbers. 5. Polynomial functions can have repeated zeros, so the fact that number is a zero doesn’t preclude it being a zero again. 7. –106 9. 0 11. 255 13. –1 15. –2, 1, [latex]\frac{1}{2}\\[/latex] 17. –2 19. –3 21. [latex]-\frac{5}{2}, \sqrt{6}, -\sqrt{6}\\[/latex] 23. [latex]2, -4, -\frac{3}{2}\\[/latex] 25. 4, –4, –5 27. [latex]5, -3, -\frac{1}{2}\\[/latex] 29. [latex]\frac{1}{2}, \frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\\[/latex] 31. [latex]\frac{3}{2}\\[/latex] 33. 2, 3, –1, –2 35. [latex]\frac{1}{2}, -\frac{1}{2}, 2, -3\\[/latex] 37. [latex]-1, -1, \sqrt{5}, -\sqrt{5}\\[/latex] 39. [latex]-\frac{3}{4}, -\frac{1}{2}\\[/latex] 41. [latex]2, 3+2i, 3 - 2i\\[/latex] 43. [latex]-\frac{2}{3}, 1+2i, 1 - 2i\\[/latex] 45. [latex]-\frac{1}{2}, 1+4i, 1 - 4i\\[/latex] 47. 1 positive, 1 negative
49. 3 or 1 positive, 0 negative
51. 0 positive, 3 or 1 negative
53. 2 or 0 positive, 2 or 0 negative
55. 2 or 0 positive, 2 or 0 negative
57. [latex]\pm 5, \pm 1, \pm \frac{5}{2}\\[/latex]
59. [latex]\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}\\[/latex]
61. [latex]1, \frac{1}{2}, -\frac{1}{3}\\[/latex]
63. [latex]2, \frac{1}{4}, -\frac{3}{2}\\[/latex]
65. [latex]\frac{5}{4}\\[/latex]
67. [latex]f\left(x\right)=\frac{4}{9}\left({x}^{3}+{x}^{2}-x - 1\right)\\[/latex]
69. [latex]f\left(x\right)=-\frac{1}{5}\left(4{x}^{3}-x\right)\\[/latex]
71. 8 by 4 by 6 inches
73. 5.5 by 4.5 by 3.5 inches
75. 8 by 5 by 3 inches
77. Radius = 6 meters, Height = 2 meters
79. Radius = 2.5 meters, Height = 4.5 metersLicenses & Attributions
CC licensed content, Shared previously
- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..
