[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522587-105":59,"doc-detail-522587-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","analyzing-and-solving-polynomial-equations-state-the-number-of-complexrealimaginary-roots-then-find-all-roots","Analyzing and Solving Polynomial Equations - State the number of complex/real/imaginary roots, then find all roots","","Worksheets for Infinite Algebra 2 focus on analyzing polynomial equations and determining root characteristics. For each listed equation, the worksheet instructs students to state the number of complex roots and the possible counts of real and imaginary roots, including how many real roots are positive or negative and which rational roots are possible. After classification, students find all roots, including complex solutions with explicit sets of values for each polynomial.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/analyzing-and-solving-polynomial-equations-state-the-number-of-complexrealimaginary-roots-then-find-all-roots/522587/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/analyzing-and-solving-polynomial-equations-state-the-number-of-complexrealimaginary-roots-then-find-all-roots/522587.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What root information must be determined before solving each polynomial equation?","Question",{"text":112,"@type":113},"The worksheet asks for the number of complex roots and the possible numbers of real and imaginary roots, plus the possible counts of positive and negative real roots and the possible rational roots.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the worksheet handle rational roots?",{"text":117,"@type":113},"For each equation, it lists a set of possible rational roots (including ± values) and then provides the actual roots after solving.",{"name":119,"@type":110,"acceptedAnswer":120},"What output does the worksheet require after classifying the roots?",{"text":121,"@type":113},"After stating root counts and possible rational roots, it requires finding all roots, including complex roots, shown as a complete roots set for each polynomial.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522587,1791498125,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kuta Software-Infinite Algebra 2 Name   \nAnalyzing and Solving Polynomial Equations Date  Period   \nState the number of complex roots, the possible number of real and imaginary roots, the possible number of positive and negative roots, and the possible rational roots for each equation. Then find all roots.  \n1) x 4 − 5x2 − 36 = 0 2) x 3 + 3x2 − 14x − 20 = 0  \n3) x 3 − 2x2 + 3x − 6 = 0 4) x 4 − 14x2 + 45 = 0  \n5) x 4 + 6x2 + 8 = 0 6) x 4 + 3x2 − 18 = 0  \n7) x 3 − 1 = 0 8) x 3 + 3x2 − x − 3 = 0  \n9) x 3 − 2x2 − 3x + 6 = 0 10) x 6 − 2x4 − 4x2 + 8 = 0  \n11) x 5 + 2x4 + 11x3 + 22x2 + 24x + 48 = 0 12) x 6 + 5x4 − 4x2 − 20 = 0  \n13) x 6 − x 4 − x 2 + 1 = 0 14) x 8 − 26x4 + 25 = 0  \nKuta Software-Infinite Algebra 2 Name   \nAnalyzing and Solving Polynomial Equations Date  Period   \nState the number of complex roots, the possible number of real and imaginary roots, the possible number of positive and negative roots, and the possible rational roots for each equation. Then find all roots.  \n1) x 4 − 5x2 − 36 = 0  \n\\# of complex roots: 4  \nPossible \\# of real roots: 4, 2, or 0 Possible \\# of imaginary roots: 4, 2, or 0 Possible \\# positive real roots: 1  \nPossible \\# negative real roots: 1  \nPossible rational roots:  \n± 1, ± 2, ± 3, ± 4, ± 6, ± 9, ± 12, ± 18, ± 36 Roots: {2i, −2i, 3, −3}  \n3) x 3 − 2x2 + 3x − 6 = 0  \n\\# of complex roots: 3 Possible \\# of real roots: 3 or 1  \nPossible \\# of imaginary roots: 2 or 0 Possible \\# positive real roots: 3 or 1 Possible \\# negative real roots: 0  \nPossible rational roots: ± 1, ± 2 , ± 3, ± 6  \nRoots: {2, i 3 , −i 3 }  \n5) x 4 + 6x2 + 8 = 0  \n\\# of complex roots: 4  \nPossible \\# of real roots: 4, 2, or 0 Possible \\# of imaginary roots: 4, 2, or 0 Possible \\# positive real roots: 0  \nPossible \\# negative real roots: 0  \nPossible rational roots: ± 1, ± 2 , ± 4, ± 8  \nRoots: {2i, −2i, i 2 , −i 2 }  \n7) x 3 − 1 = 0  \n\\# of complex roots: 3 Possible \\# of real roots: 3 or 1  \nPossible \\# of imaginary roots: 2 or 0 Possible \\# positive real roots: 1  \nPossible \\# negative real roots: 0  \nPossible rational roots: ± 1  \nRoots: { 1, −1~~ ~~+2i~~ ~~3~~ ~~ , −1~~ ~~−2i~~ ~~3~~ ~~ }  \n2) x 3 + 3x2 − 14x − 20 = 0  \n\\# of complex roots: 3 Possible \\# of real roots: 3 or 1  \nPossible \\# of imaginary roots: 2 or 0  \nPossible \\# positive real roots: 1  \nPossible \\# negative real roots: 2 or 0  \nPossible rational roots:  \n± 1, ± 2, ± 4, ± 5, ± 10, ± 20 Roots: {−5, 1 + 5 , 1 − 5 }  \n4) x 4 − 14x2 + 45 = 0  \n\\# of complex roots: 4  \nPossible \\# of real roots: 4, 2, or 0  \nPossible \\# of imaginary roots: 4, 2, or 0 Possible \\# positive real roots: 2 or 0  \nPossible \\# negative real roots: 2 or 0  \nPossible rational roots:  \n± 1, ± 3, ± 5, ± 9, ± 15, ± 45 Roots: { 5 , − 5 , 3, −3 }  \n6) x 4 + 3x2 − 18 = 0  \n\\# of complex roots: 4  \nPossible \\# of real roots: 4, 2, or 0  \nPossible \\# of imaginary roots: 4, 2, or 0 Possible \\# positive real roots: 1  \nPossible \\# negative real roots: 1  \nPossible rational roots: ± 1, ± 2 , ± 3, ± 6, ± 9, ± 18  \nRoots: { 3 , − 3 , i 6 , −i 6 }  \n8) x 3 + 3x2 − x − 3 = 0  \n\\# of complex roots: 3 Possible \\# of real roots: 3 or 1  \nPossible \\# of imaginary roots: 2 or 0  \nPossible \\# positive real roots: 1  \nPossible \\# negative real roots: 2 or 0  \nPossible rational roots: ± 1, ± 3  \nRoots: {−3, 1, −1}  \n9) x 3 − 2x2 − 3x + 6 = 0  \n\\# of complex roots: 3 Possible \\# of real roots: 3 or 1  \nPossible \\# of imaginary roots: 2 or 0 Possible \\# positive real roots: 2 or 0 Possible \\# negative real roots: 1  \nPossible rational roots: ± 1, ± 2 , ± 3, ± 6  \nRoots: {2, 3 , − 3 }  \n11) x 5 + 2x4 + 11x3 + 22x2 + 24x + 48 = 0  \n\\# of complex roots: 5  \nPossible \\# of real roots: 5, 3, or 1  \nPossible \\# of imaginary roots: 4, 2, or 0 Possible \\# positive real roots: 0  \nPossible \\# negative real roots: 5, 3, or 1 Possible rational roots:  \n± 1, ± 2, ± 3, ± 4, ± 6, ± 8, ± 12, ± 16, ± 24, ± 48 Roots: {−2, i 3 , −i 3 , 2i 2 , −2i 2 }  \n13) x 6 − x 4 − x 2 + 1 = 0  \n\\# of complex roots: 6  \nPossible \\# of r","cbCairf3RxNrBT1D","https://ap.wps.com/l/cbCairf3RxNrBT1D","pdf",36853,"English","# Polynomial Root Analysis and Solving\n## Root counting: complex, real, imaginary\n## Positive/negative real roots and possible rational roots\n## Finding all roots for each equation","[{\"question\":\"What root information must be determined before solving each polynomial equation?\",\"answer\":\"The worksheet asks for the number of complex roots and the possible numbers of real and imaginary roots, plus the possible counts of positive and negative real roots and the possible rational roots.\"},{\"question\":\"How does the worksheet handle rational roots?\",\"answer\":\"For each equation, it lists a set of possible rational roots (including ± values) and then provides the actual roots after solving.\"},{\"question\":\"What output does the worksheet require after classifying the roots?\",\"answer\":\"After stating root counts and possible rational roots, it requires finding all roots, including complex roots, shown as a complete roots set for each polynomial.\"}]","Analyzing and Solving Polynomial Equations - State the number of complex/real/imaginary roots, then find all roots | PDF",1791425947]