{"id":192,"date":"2022-04-13T10:17:40","date_gmt":"2022-04-13T10:17:40","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=192"},"modified":"2024-08-25T08:02:54","modified_gmt":"2024-08-25T08:02:54","slug":"j-4-solve-a-quadratic-equation-using-the-zero-product-property","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-4-solve-a-quadratic-equation-using-the-zero-product-property\/","title":{"rendered":"J.4 Solve a quadratic equation using the zero product property"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Solve a quadratic equation using the zero product property<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-0f87aba31ce34ea0a5a7ed89c94d5f7d\" style=\"color:#29e075\"><strong>Understanding the Zero Product Property<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.<\/li>\n\n\n\n<li>This property is used to solve quadratic equations that can be factored into the form (a + b)(c + d) = 0.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d1fa4a6e37c72ce7b00900b7429e2d92\" style=\"color:#4d9100\"><strong>Steps to Solve Using the Zero Product Property<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Factor the Quadratic Equation:<\/strong> Express the quadratic equation in the form (a + b)(c + d) = 0.<\/li>\n\n\n\n<li><strong>Set Each Factor Equal to Zero:<\/strong> Create two separate equations:\n<ul class=\"wp-block-list\">\n<li>a + b = 0<\/li>\n\n\n\n<li>c + d = 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Solve Each Equation:<\/strong> Solve each equation independently to find the values of x that make the factors zero.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-319bdb25c4292ebbc43384dee1d288e2\" style=\"color:#f88a23\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Solve: x\u00b2 &#8211; 4x + 3 = 0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Factor the equation: (x &#8211; 1)(x &#8211; 3) = 0<\/li>\n\n\n\n<li>Step 2: Set each factor equal to zero:\n<ul class=\"wp-block-list\">\n<li>x &#8211; 1 = 0<\/li>\n\n\n\n<li>x &#8211; 3 = 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Step 3: Solve each equation:\n<ul class=\"wp-block-list\">\n<li>x = 1<\/li>\n\n\n\n<li>x = 3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f520925bfcd13b03a81b70ffaaa53bd8\" style=\"color:#3f23c8\"><strong>Key Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The Zero Product Property is a powerful tool for solving quadratic equations that can be factored.<\/li>\n\n\n\n<li>Factoring the quadratic equation is crucial for applying this method.<\/li>\n\n\n\n<li>Setting each factor equal to zero creates two separate equations to solve.<\/li>\n\n\n\n<li>The solutions to the equations represent the values of x that make the original quadratic equation true.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1b3f4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve for&nbsp;<em>r<\/em>.<\/strong><\/p>\n\n\n\n<p>(<em>r<\/em>&nbsp;+ 3)(<em>r<\/em>&nbsp;+ 9)&nbsp;= 0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>r<\/em>&nbsp;=&nbsp;________&nbsp;or&nbsp;<em>r<\/em>&nbsp;=________<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the Zero Product Property, if&nbsp;(<em>r<\/em>&nbsp;+ 3)(<em>r<\/em>&nbsp;+ 9)&nbsp;= 0,&nbsp;then&nbsp;(<em>r<\/em>&nbsp;+ 3)&nbsp;must be 0 or&nbsp;(<em>r<\/em>&nbsp;+ 9)&nbsp;must be 0. Write two equations and solve for&nbsp;<em>r<\/em>.<\/p>\n\n\n\n<p>r+3=0     or       r+9=0<\/p>\n\n\n\n<p>r=-3                  r=-9<\/p>\n\n\n\n<p>The solution is <em>r<\/em>&nbsp;=&nbsp;-3 or <em>r<\/em>&nbsp;=&nbsp;-9.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9db5f4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve for&nbsp;<em>n<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-bb4a1a666a4bb0324218f2ddc538820f\"><em>n<\/em>(<em>n<\/em>&nbsp;+ 2)&nbsp;= 0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>n<\/em>&nbsp;=&nbsp;________&nbsp;or&nbsp;<em>n<\/em>&nbsp;=&nbsp;________<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the Zero Product Property, if&nbsp;<em>n<\/em>(<em>n<\/em>&nbsp;+ 2)&nbsp;= 0,&nbsp;then&nbsp;<em>n<\/em>&nbsp;must be 0 or&nbsp;(<em>n<\/em>&nbsp;+ 2)&nbsp;must be 0. Write two equations and solve for&nbsp;<em>n<\/em>.<\/p>\n\n\n\n<p>n=0               or            n+2=0<\/p>\n\n\n\n<p>                                      n=-2<\/p>\n\n\n\n<p>The solution is <em>n<\/em>&nbsp;=&nbsp;0 or <em>n<\/em>&nbsp;=&nbsp;-2.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a2f2ca\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve for&nbsp;<em>q<\/em>.<\/strong><\/p>\n\n\n\n<p>(<em>q<\/em>&nbsp;+ 4)(<em>q<\/em>&nbsp;\u2212 8)&nbsp;= 0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>q<\/em>&nbsp;=________or&nbsp;<em>q<\/em>&nbsp;=&nbsp;________<\/p>\n<\/div><\/div>\n\n\n\n<p>According to the Zero Product Property, if&nbsp;(<em>q<\/em>&nbsp;+ 4)(<em>q<\/em>&nbsp;\u2212 8)&nbsp;= 0,&nbsp;then&nbsp;(<em>q<\/em>&nbsp;+ 4)&nbsp;must be 0 or&nbsp;(<em>q<\/em>&nbsp;\u2212 8)&nbsp;must be 0. Write two equations and solve for&nbsp;<em>q<\/em>.<\/p>\n\n\n\n<p>q+4=0                or       q-8=0<\/p>\n\n\n\n<p>q=-4                                q=-8<\/p>\n\n\n\n<p>The solution is <em>q<\/em>&nbsp;=&nbsp;-4 or <em>q<\/em>&nbsp;=&nbsp;8.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76681\/391\/983\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-51.png\" alt=\"\" class=\"wp-image-6942\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-51.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-51-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-51-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76716\/162\/232\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-69.png\" alt=\"\" class=\"wp-image-6943\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-69.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-69-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-69-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve a quadratic equation using the zero product property Key Notes : Understanding the Zero Product Property Steps to Solve Using the Zero Product Property Example Solve: x\u00b2 &#8211; 4x + 3 = 0 Key Points Learn with an example Solve for&nbsp;r. (r&nbsp;+ 3)(r&nbsp;+ 9)&nbsp;= 0 Write your answers as integers or as proper or<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-4-solve-a-quadratic-equation-using-the-zero-product-property\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.4 Solve a quadratic equation using the zero product property&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-192","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=192"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/192\/revisions"}],"predecessor-version":[{"id":13682,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/192\/revisions\/13682"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}