{"id":1405,"date":"2015-11-12T18:35:29","date_gmt":"2015-11-12T18:35:29","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1405"},"modified":"2017-03-31T23:05:09","modified_gmt":"2017-03-31T23:05:09","slug":"solutions-40","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-40\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]f\\left(-3\\right)=-412[\/latex]\r\n\r\n2.\u00a0The zeros are 2, \u20132, and \u20134.\r\n\r\n3.\u00a0There are no rational zeros.\r\n\r\n4.\u00a0The zeros are [latex]\\text{-4, }\\frac{1}{2},\\text{ and 1}\\text{.}[\/latex]\r\n\r\n5.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{2}{x}^{3}+\\frac{5}{2}{x}^{2}-2x+10[\/latex]\r\n\r\n6.\u00a0There 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.\r\n\r\n7.\u00a03 meters by 4 meters by 7 meters\r\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1. The theorem can be used to evaluate a polynomial.\r\n\r\n3.\u00a0Rational zeros can be expressed as fractions whereas real zeros include irrational numbers.\r\n\r\n5.\u00a0Polynomial functions can have repeated zeros, so the fact that number is a zero doesn\u2019t preclude it being a zero again.\r\n\r\n7. \u2013106\r\n\r\n9.\u00a00\r\n\r\n11.\u00a0255\r\n\r\n13. \u20131\r\n\r\n15. \u20132, 1, [latex]\\frac{1}{2}[\/latex]\r\n\r\n17. \u20132\r\n\r\n19. \u20133\r\n\r\n21.\u00a0[latex]-\\frac{5}{2}, \\sqrt{6}, -\\sqrt{6}[\/latex]\r\n\r\n23.\u00a0[latex]2, -4, -\\frac{3}{2}[\/latex]\r\n\r\n25. 4, \u20134, \u20135\r\n\r\n27.\u00a0[latex]5, -3, -\\frac{1}{2}[\/latex]\r\n\r\n29.\u00a0[latex]\\frac{1}{2}, \\frac{1+\\sqrt{5}}{2}, \\frac{1-\\sqrt{5}}{2}[\/latex]\r\n\r\n31.\u00a0[latex]\\frac{3}{2}[\/latex]\r\n\r\n33. 2, 3, \u20131, \u20132\r\n\r\n35.\u00a0[latex]\\frac{1}{2}, -\\frac{1}{2}, 2, -3[\/latex]\r\n\r\n37.\u00a0[latex]-1, -1, \\sqrt{5}, -\\sqrt{5}[\/latex]\r\n\r\n39.\u00a0[latex]-\\frac{3}{4}, -\\frac{1}{2}[\/latex]\r\n\r\n41.\u00a0[latex]2, 3+2i, 3 - 2i[\/latex]\r\n\r\n43.\u00a0[latex]-\\frac{2}{3}, 1+2i, 1 - 2i[\/latex]\r\n\r\n45.\u00a0[latex]-\\frac{1}{2}, 1+4i, 1 - 4i[\/latex]\r\n\r\n47.\u00a01 positive, 1 negative\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201604\/CNX_PreCalc_Figure_03_06_202.jpg\" alt=\"Graph of f(x)=x^4-x^2-1.\" data-media-type=\"image\/jpg\"\/>\r\n\r\n49.\u00a03 or 1 positive, 0 negative\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201605\/CNX_PreCalc_Figure_03_06_204.jpg\" alt=\"Graph of f(x)=x^3-2x^2+x-1.\" data-media-type=\"image\/jpg\"\/>\r\n\r\n51.\u00a00 positive, 3 or 1 negative\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201608\/CNX_PreCalc_Figure_03_06_206.jpg\" alt=\"Graph of f(x)=2x^3+37x^2+200x+300.\" data-media-type=\"image\/jpg\"\/>\r\n\r\n53.\u00a02 or 0 positive, 2 or 0 negative\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201610\/CNX_PreCalc_Figure_03_06_208.jpg\" alt=\"Graph of f(x)=2x^4-5x^3-5x^2+5x+3.\" data-media-type=\"image\/jpg\"\/>\r\n\r\n55.\u00a02 or 0 positive, 2 or 0 negative\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201611\/CNX_PreCalc_Figure_03_06_210.jpg\" alt=\"Graph of f(x)=10x^4-21x^2+11.\" data-media-type=\"image\/jpg\"\/>\r\n\r\n57.\u00a0[latex]\\pm 5, \\pm 1, \\pm \\frac{5}{2}[\/latex]\r\n\r\n59.\u00a0[latex]\\pm 1, \\pm \\frac{1}{2}, \\pm \\frac{1}{3}, \\pm \\frac{1}{6}[\/latex]\r\n\r\n61.\u00a0[latex]1, \\frac{1}{2}, -\\frac{1}{3}[\/latex]\r\n\r\n63.\u00a0[latex]2, \\frac{1}{4}, -\\frac{3}{2}[\/latex]\r\n\r\n65.\u00a0[latex]\\frac{5}{4}[\/latex]\r\n\r\n67.\u00a0[latex]f\\left(x\\right)=\\frac{4}{9}\\left({x}^{3}+{x}^{2}-x - 1\\right)[\/latex]\r\n\r\n69.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{5}\\left(4{x}^{3}-x\\right)[\/latex]\r\n\r\n71.\u00a08 by 4 by 6 inches\r\n\r\n73.\u00a05.5 by 4.5 by 3.5 inches\r\n\r\n75.\u00a08 by 5 by 3 inches\r\n\r\n77.\u00a0Radius = 6 meters, Height = 2 meters\r\n\r\n79.\u00a0Radius = 2.5 meters, Height = 4.5 meters","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1.\u00a0[latex]f\\left(-3\\right)=-412[\/latex]<\/p>\n<p>2.\u00a0The zeros are 2, \u20132, and \u20134.<\/p>\n<p>3.\u00a0There are no rational zeros.<\/p>\n<p>4.\u00a0The zeros are [latex]\\text{-4, }\\frac{1}{2},\\text{ and 1}\\text{.}[\/latex]<\/p>\n<p>5.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{2}{x}^{3}+\\frac{5}{2}{x}^{2}-2x+10[\/latex]<\/p>\n<p>6.\u00a0There 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.<\/p>\n<p>7.\u00a03 meters by 4 meters by 7 meters<\/p>\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1. The theorem can be used to evaluate a polynomial.<\/p>\n<p>3.\u00a0Rational zeros can be expressed as fractions whereas real zeros include irrational numbers.<\/p>\n<p>5.\u00a0Polynomial functions can have repeated zeros, so the fact that number is a zero doesn\u2019t preclude it being a zero again.<\/p>\n<p>7. \u2013106<\/p>\n<p>9.\u00a00<\/p>\n<p>11.\u00a0255<\/p>\n<p>13. \u20131<\/p>\n<p>15. \u20132, 1, [latex]\\frac{1}{2}[\/latex]<\/p>\n<p>17. \u20132<\/p>\n<p>19. \u20133<\/p>\n<p>21.\u00a0[latex]-\\frac{5}{2}, \\sqrt{6}, -\\sqrt{6}[\/latex]<\/p>\n<p>23.\u00a0[latex]2, -4, -\\frac{3}{2}[\/latex]<\/p>\n<p>25. 4, \u20134, \u20135<\/p>\n<p>27.\u00a0[latex]5, -3, -\\frac{1}{2}[\/latex]<\/p>\n<p>29.\u00a0[latex]\\frac{1}{2}, \\frac{1+\\sqrt{5}}{2}, \\frac{1-\\sqrt{5}}{2}[\/latex]<\/p>\n<p>31.\u00a0[latex]\\frac{3}{2}[\/latex]<\/p>\n<p>33. 2, 3, \u20131, \u20132<\/p>\n<p>35.\u00a0[latex]\\frac{1}{2}, -\\frac{1}{2}, 2, -3[\/latex]<\/p>\n<p>37.\u00a0[latex]-1, -1, \\sqrt{5}, -\\sqrt{5}[\/latex]<\/p>\n<p>39.\u00a0[latex]-\\frac{3}{4}, -\\frac{1}{2}[\/latex]<\/p>\n<p>41.\u00a0[latex]2, 3+2i, 3 - 2i[\/latex]<\/p>\n<p>43.\u00a0[latex]-\\frac{2}{3}, 1+2i, 1 - 2i[\/latex]<\/p>\n<p>45.\u00a0[latex]-\\frac{1}{2}, 1+4i, 1 - 4i[\/latex]<\/p>\n<p>47.\u00a01 positive, 1 negative<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201604\/CNX_PreCalc_Figure_03_06_202.jpg\" alt=\"Graph of f(x)=x^4-x^2-1.\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>49.\u00a03 or 1 positive, 0 negative<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201605\/CNX_PreCalc_Figure_03_06_204.jpg\" alt=\"Graph of f(x)=x^3-2x^2+x-1.\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>51.\u00a00 positive, 3 or 1 negative<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201608\/CNX_PreCalc_Figure_03_06_206.jpg\" alt=\"Graph of f(x)=2x^3+37x^2+200x+300.\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>53.\u00a02 or 0 positive, 2 or 0 negative<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201610\/CNX_PreCalc_Figure_03_06_208.jpg\" alt=\"Graph of f(x)=2x^4-5x^3-5x^2+5x+3.\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>55.\u00a02 or 0 positive, 2 or 0 negative<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201611\/CNX_PreCalc_Figure_03_06_210.jpg\" alt=\"Graph of f(x)=10x^4-21x^2+11.\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>57.\u00a0[latex]\\pm 5, \\pm 1, \\pm \\frac{5}{2}[\/latex]<\/p>\n<p>59.\u00a0[latex]\\pm 1, \\pm \\frac{1}{2}, \\pm \\frac{1}{3}, \\pm \\frac{1}{6}[\/latex]<\/p>\n<p>61.\u00a0[latex]1, \\frac{1}{2}, -\\frac{1}{3}[\/latex]<\/p>\n<p>63.\u00a0[latex]2, \\frac{1}{4}, -\\frac{3}{2}[\/latex]<\/p>\n<p>65.\u00a0[latex]\\frac{5}{4}[\/latex]<\/p>\n<p>67.\u00a0[latex]f\\left(x\\right)=\\frac{4}{9}\\left({x}^{3}+{x}^{2}-x - 1\\right)[\/latex]<\/p>\n<p>69.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{5}\\left(4{x}^{3}-x\\right)[\/latex]<\/p>\n<p>71.\u00a08 by 4 by 6 inches<\/p>\n<p>73.\u00a05.5 by 4.5 by 3.5 inches<\/p>\n<p>75.\u00a08 by 5 by 3 inches<\/p>\n<p>77.\u00a0Radius = 6 meters, Height = 2 meters<\/p>\n<p>79.\u00a0Radius = 2.5 meters, Height = 4.5 meters<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1405\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1405","chapter","type-chapter","status-publish","hentry"],"part":1376,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1405","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1405\/revisions"}],"predecessor-version":[{"id":2945,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1405\/revisions\/2945"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1376"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1405\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=1405"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1405"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1405"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=1405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}