[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522786-105":3,"doc-detail-522786-en":81,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","kuta-software-infinite-algebra-2-the-discriminant-worksheet","Kuta Software - Infinite Algebra 2 - The Discriminant - Worksheet","","Quadratic-equation worksheet on finding the discriminant and interpreting it to classify solutions. Problems 1–6 ask for the discriminant values. Problems 7–14 require discriminant calculation and stating how many solutions are real or imaginary. Problems 15–22 extend this to rational, irrational, and imaginary counts. Two critical-thinking prompts ask students to construct a quadratic with two imaginary solutions and explain why a quadratic cannot have exactly one imaginary solution.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/kuta-software-infinite-algebra-2-the-discriminant-worksheet/522786/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/kuta-software-infinite-algebra-2-the-discriminant-worksheet/522786.png","ImageObject",300,407,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-05","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the discriminant task in this worksheet?","Question",{"text":63,"@type":64},"Students compute the discriminant for each quadratic equation to determine solution behavior.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you classify solutions as real or imaginary?",{"text":68,"@type":64},"After finding the discriminant, the worksheet requires stating the number of real versus imaginary solutions for each equation.",{"name":70,"@type":61,"acceptedAnswer":71},"What do the critical thinking questions ask?",{"text":72,"@type":64},"One question asks students to write a quadratic with two imaginary solutions, and another asks them to explain why a quadratic cannot have exactly one imaginary solution.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522786,1791671152,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":91,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":92,"faqs":93,"seo_title":94,"seo_description":12,"update_tm":95,"read_time":96,"preview_page_count":4},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Algebra 2 Name___________________________________  \nUnderstanding the Discriminant Date________________ Period____  \nFind the value of the discriminant of each quadratic equation.  \n1) 6 p2 − 2 p − 3 = 0 2) −2x2 − x − 1 = 0  \n3) −4m2 − 4m + 5 = 0 4) 5b2 + b − 2 = 0  \n5) r2 + 5r + 2 = 0 6) 2 p2 + 5 p − 4 = 0  \nFind the discriminant of each quadratic equation then state the numberof real and imaginary solutions.  \n7) 9n2 − 3n − 8 = −10 8) −2x2 − 8x − 14 = −6  \n9) 9m2 + 6m + 6 = 5 10) 4a2 = 8a − 4  \n11) −9b2 = −8b + 8 12) −x2 − 9 = 6x  \n13) −4r2 − 4r = 6 14) 8b2 − 6b + 3 = 5b2  \nFind the discriminant then state the number of rational, irrational, and imaginary solutions.  \n15) −6x2 − 6 = −7x − 9 16) 4k2 + 5k + 4 = −3k  \n17) −7n2 + 16n = 8n 18) 2x2 = 10x + 5  \n19) −10n2 − 3n − 9 = −2n 20) −9r2 − 8r − 1 = r − r2 − 9  \n21) −3 p2 + 10 p + 5 = −8 p2 22) m 2 + 5m = 2m2  \nCritical thinking questions:  \n23) Write a quadratic equation that has two 24) In your own words explain why a quadratic  \nimaginary solutions. equation can't have one imaginary solution.  \nKuta Software-Infinite Algebra 2 Name___________________________________  \nUnderstanding the Discriminant Date________________ Period____  \nFind the value of the discriminant of each quadratic equation.  \n1) 6 p2 − 2 p − 3 = 0 2) −2x2 − x − 1 = 0  \n76 −7  \n3) −4m2 − 4m + 5 = 0 4) 5b2 + b − 2 = 0  \n96 41  \n5) r2 + 5r + 2 = 0 6) 2 p2 + 5 p − 4 = 0  \n17 57  \nFind the discriminant of each quadratic equation then state the numberof real and imaginary solutions.  \n7) 9n2 − 3n − 8 = −10 8) −2x2 − 8x − 14 = −6  \n−63; two imaginary solutions 0; one real solution  \n9) 9m2 + 6m + 6 = 5 10) 4a2 = 8a − 4  \n0; one real solution 0; one real solution  \n11) −9b2 = −8b + 8 12) −x2 − 9 = 6x  \n−224; two imaginary solutions 0; one real solution  \n13) −4r2 − 4r = 6  \n−80; two imaginary solutions  \n14) 8b2 − 6b + 3 = 5b2  \n0; one real solution  \nFind the discriminant then state the number of rational, irrational, and imaginary solutions.  \n15) −6x2 − 6 = −7x − 9 16) 4k2 + 5k + 4 = −3k  \n121; two rational solutions 0; one rational solution  \n17) −7n2 + 16n = 8n 18) 2x2 = 10x + 5  \n64; two rational solutions 140; two irrational solutions  \n19) −10n2 − 3n − 9 = −2n 20) −9r2 − 8r − 1 = r − r2 − 9  \n−359; two imaginary solutions 337; two irrational solutions  \n21) −3 p2 + 10 p + 5 = −8 p2 22) m 2 + 5m = 2m2  \n0; one rational solution 25; two rational solutions  \nCritical thinking questions:  \n23) Write a quadratic equation that has two 24) In your own words explain why a quadratic  \nimaginary solutions. equation can't have one imaginary solution.  \nMany answers. Ex: x2 + x + 1 = 0 Answers vary.  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiaBWoFt5HM3A","https://ap.wps.com/l/cbCaiaBWoFt5HM3A","pdf",34132,"English","# Understanding the Discriminant\n## Find the value of the discriminant\n## Discriminant and solution types: real vs. imaginary\n## Discriminant and solution types: rational, irrational, and imaginary\n## Critical thinking questions","[{\"question\":\"What is the discriminant task in this worksheet?\",\"answer\":\"Students compute the discriminant for each quadratic equation to determine solution behavior.\"},{\"question\":\"How do you classify solutions as real or imaginary?\",\"answer\":\"After finding the discriminant, the worksheet requires stating the number of real versus imaginary solutions for each equation.\"},{\"question\":\"What do the critical thinking questions ask?\",\"answer\":\"One question asks students to write a quadratic with two imaginary solutions, and another asks them to explain why a quadratic cannot have exactly one imaginary solution.\"}]","Kuta Software - Infinite Algebra 2 - The Discriminant - Worksheet | PDF",1791426171,10,{"code":4,"msg":82,"data":98},[99,103,107,110,115,119,124,129,134,137,140],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":108,"slug":109},70,"exam",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":125,"doc_module":4,"doc_module_name":25,"category_name":126,"show_sort_weight":127,"slug":128},8,"Research & Report",30,"research-report",{"id":130,"doc_module":4,"doc_module_name":25,"category_name":131,"show_sort_weight":132,"slug":133},9,"Religion & Spirituality",20,"religion-spirituality",{"id":132,"doc_module":4,"doc_module_name":25,"category_name":135,"show_sort_weight":132,"slug":136},"World Cup","world-cup",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":138,"show_sort_weight":96,"slug":139},"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":25,"category_name":142,"show_sort_weight":111,"slug":143},19,"General","general"]