{"id":1656,"date":"2020-04-06T06:42:53","date_gmt":"2020-04-06T06:42:53","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1656"},"modified":"2020-04-06T06:44:41","modified_gmt":"2020-04-06T06:44:41","slug":"ibdp-past-year-exam-questions-polynomials-2","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/polynomials\/ibdp-past-year-exam-questions-polynomials-2\/","title":{"rendered":"IBDP Past Year Exam Questions 2- Polynomials"},"content":{"rendered":"<p><strong>1.[M14\/P1\/TZ1]<\/strong><\/p>\r\n<p>When the polynomial\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>3<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><mi>a<\/mi><mi>x<\/mi><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><mi>b<\/mi><\/math>\r\n is divided by\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>&#160;<\/mo><mo>&#8211;<\/mo><mo>&#160;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n , the remainder is 2, and when divided by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n \u00a0, it is 5. Find the value of<em> a<\/em> and the value of<em> b<\/em> .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link1-link-1656\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1656, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1656\">Solution<\/span><\/a><\/div><div id=\"link1-content-1656\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1657\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-39.jpg\" alt=\"\" width=\"984\" height=\"154\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-39.jpg 984w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-39-300x47.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-39-768x120.jpg 768w\" sizes=\"auto, (max-width: 984px) 100vw, 984px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>2.[M14\/P1\/TZ1]<\/strong><\/p>\r\n<p>The equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><mn>48<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><mn>100<\/mn><mi>x<\/mi><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><mn>2<\/mn><mo>=<\/mo><mi>a<\/mi><\/math>\r\n has roots\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mn>1<\/mn><\/msub><mo>&#160;<\/mo><mo>,<\/mo><mo>&#160;<\/mo><msub><mi>r<\/mi><mn>2<\/mn><\/msub><\/math>\r\n and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mn>3<\/mn><\/msub><\/math>\r\n . Given that\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mn>1<\/mn><\/msub><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><msub><mi>r<\/mi><mn>2<\/mn><\/msub><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><msub><mi>r<\/mi><mn>3<\/mn><\/msub><mo>&#160;<\/mo><mo>+<\/mo><mo>&#160;<\/mo><msub><mi>r<\/mi><mn>1<\/mn><\/msub><msub><mi>r<\/mi><mn>2<\/mn><\/msub><msub><mi>r<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mn>0<\/mn><\/math>\r\n , find the value of <em>a<\/em> .\u00a0 \u00a0 [6 marks]<\/p>\r\n<div id=\"link1-link-1656\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1656, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1656\">Solution<\/span><\/a><\/div><div id=\"link1-content-1656\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1658\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-40.jpg\" alt=\"\" width=\"995\" height=\"270\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-40.jpg 995w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-40-300x81.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-40-768x208.jpg 768w\" sizes=\"auto, (max-width: 995px) 100vw, 995px\" \/><\/p>\r\n<p>\u00a0<\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1.[M14\/P1\/TZ1] When the polynomial\u00a0 3&#215;3&#160;+&#160;ax&#160;+&#160;b is divided by\u00a0 x&#160;&#8211;&#160;2 , the remainder is 2, and when divided by x+1 \u00a0, it is 5. Find the value of a and the value of b .\u00a0 \u00a0[5 marks] 2.[M14\/P1\/TZ1] The equation\u00a0 5&#215;3&#160;+&#160;48&#215;2&#160;+&#160;100x&#160;+&#160;2=a has roots\u00a0 r1&#160;,&#160;r2 and\u00a0 r3 . Given that\u00a0 r1&#160;+&#160;r2&#160;+&#160;r3&#160;+&#160;r1r2r3=0 , find the value of a [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1656","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-polynomials","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1656","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1656"}],"version-history":[{"count":4,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1656\/revisions"}],"predecessor-version":[{"id":1662,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1656\/revisions\/1662"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}