{"id":202,"date":"2022-04-13T10:19:12","date_gmt":"2022-04-13T10:19:12","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=202"},"modified":"2024-08-25T07:43:15","modified_gmt":"2024-08-25T07:43:15","slug":"j-9-using-the-discriminant","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-9-using-the-discriminant\/","title":{"rendered":"J.9 Using the discriminant"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Using the discriminant<\/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-4f360199f6a24707debf0d8989cd654f\" style=\"color:#ff4747\"><strong>Understanding the Discriminant<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The discriminant is the expression under the square root in the quadratic formula: b\u00b2 &#8211; 4ac.<\/li>\n\n\n\n<li>It provides valuable information about the nature of the solutions to a quadratic equation.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-30578a55684f8c977ae39be11ba3d4a7\" style=\"color:#c3ee17\"><strong>Interpreting the Discriminant<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive Discriminant (b\u00b2 &#8211; 4ac &gt; 0):<\/strong> The quadratic equation has two distinct real roots. This means the parabola intersects the x-axis at two different points.<\/li>\n\n\n\n<li><strong>Zero Discriminant (b\u00b2 &#8211; 4ac = 0):<\/strong> The quadratic equation has one repeated real root. This means the parabola touches the x-axis at exactly one point.<\/li>\n\n\n\n<li><strong>Negative Discriminant (b\u00b2 &#8211; 4ac &lt; 0):<\/strong> The quadratic equation has no real roots. This means the parabola does not intersect the x-axis. The solutions are complex numbers.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-9c5bcfdaeb8f74289a48eb4ed4945e29\" style=\"color:#e61414\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Consider the quadratic equation: 2x\u00b2 &#8211; 5x + 3 = 0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calculate the discriminant: b\u00b2 &#8211; 4ac = (-5)\u00b2 &#8211; 4(2)(3) = 1<\/li>\n\n\n\n<li>Since the discriminant is positive, the equation has two distinct real roots.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-99737158f90f7a7f64a65292706e4715\" style=\"color:#72f824\"><strong>Key Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The discriminant is a powerful tool for analyzing quadratic equations.<\/li>\n\n\n\n<li>It helps to determine the number and nature of the solutions without actually solving the equation.<\/li>\n\n\n\n<li>Understanding the discriminant can save time and effort when solving quadratic equations.<\/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:#ccf2a9\"><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 class=\"has-text-color has-link-color wp-elements-e2d2e179b5047886be700d6dcbaf823f\" style=\"color:#b00012\"><strong>Find&nbsp;the&nbsp;discriminant.<\/strong><\/p>\n\n\n\n<p>2v<sup>2<\/sup>+v+9=0________<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the discriminant of&nbsp;2v2+v+9=0.<\/p>\n\n\n\n<p>b<sup>2<\/sup>\u20134ac<\/p>\n\n\n\n<p>=<strong>1<\/strong><sup>2<\/sup>\u20134(<strong>2<\/strong>)(<strong>9<\/strong>)      Plug&nbsp;in&nbsp;a=2,&nbsp;b=1&nbsp;and&nbsp;c=9<\/p>\n\n\n\n<p>=1\u201372       Multiply<\/p>\n\n\n\n<p>=\u201371         Subtract<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c5cdf1\"><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 class=\"has-text-color has-link-color wp-elements-e2d2e179b5047886be700d6dcbaf823f\" style=\"color:#b00012\"><strong>Find&nbsp;the&nbsp;discriminant.<\/strong><\/p>\n\n\n\n<p>7y<sup>2<\/sup>\u20133y+2=0________<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the discriminant of&nbsp;7y<sup>2<\/sup>\u20133y+2=0.<\/p>\n\n\n\n<p>b<sup>2<\/sup>\u20134ac<\/p>\n\n\n\n<p>=(\u2013<strong>3<\/strong>)<sup>2<\/sup>\u20134(<strong>7<\/strong>)(<strong>2<\/strong>)       Plug&nbsp;in&nbsp;a=7,&nbsp;b=\u20133&nbsp;and&nbsp;c=2<\/p>\n\n\n\n<p>=9\u201356      Multiply<\/p>\n\n\n\n<p>=\u201347     Subtract<\/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:#eeaec0\"><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 class=\"has-text-color has-link-color wp-elements-e2d2e179b5047886be700d6dcbaf823f\" style=\"color:#b00012\"><strong>Find&nbsp;the&nbsp;discriminant.<\/strong><\/p>\n\n\n\n<p>3u<sup>2<\/sup>+6u+3=0________<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the discriminant of&nbsp;3u<sup>2<\/sup>+6u+3=0.<\/p>\n\n\n\n<p>b<sup>2<\/sup>\u20134ac<\/p>\n\n\n\n<p>=<strong>6<\/strong><sup>2<\/sup>\u20134(<strong>3<\/strong>)(<strong>3<\/strong>)       Plug&nbsp;in&nbsp;a=3,&nbsp;b=6&nbsp;and&nbsp;c=3<\/p>\n\n\n\n<p>=36\u201336         Multiply<\/p>\n\n\n\n<p>=0             Subtract<\/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\/76706\/917\/558\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-56.png\" alt=\"\" class=\"wp-image-6969\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-56.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-56-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-56-150x150.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\/76724\/710\/707\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74.png\" alt=\"\" class=\"wp-image-6970\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Using the discriminant Key Notes : Understanding the Discriminant Interpreting the Discriminant Example Consider the quadratic equation: 2x\u00b2 &#8211; 5x + 3 = 0 Key Points Learn with an example Find&nbsp;the&nbsp;discriminant. 2v2+v+9=0________ Find&nbsp;the discriminant of&nbsp;2v2+v+9=0. b2\u20134ac =12\u20134(2)(9) Plug&nbsp;in&nbsp;a=2,&nbsp;b=1&nbsp;and&nbsp;c=9 =1\u201372 Multiply =\u201371 Subtract Find&nbsp;the&nbsp;discriminant. 7y2\u20133y+2=0________ Find&nbsp;the discriminant of&nbsp;7y2\u20133y+2=0. b2\u20134ac =(\u20133)2\u20134(7)(2) Plug&nbsp;in&nbsp;a=7,&nbsp;b=\u20133&nbsp;and&nbsp;c=2 =9\u201356 Multiply =\u201347 Subtract Find&nbsp;the&nbsp;discriminant.<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-9-using-the-discriminant\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.9 Using the discriminant&#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-202","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202","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=202"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions"}],"predecessor-version":[{"id":13674,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions\/13674"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}