{"id":126622,"date":"2022-12-27T12:46:27","date_gmt":"2022-12-27T07:16:27","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=126622"},"modified":"2023-04-06T13:37:04","modified_gmt":"2023-04-06T08:07:04","slug":"nature-of-roots-of-a-quadratic-equation-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/","title":{"rendered":"Nature of Roots of a Quadratic Equation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Nature_of_Roots_of_a_Quadratic_Equations\" title=\"Nature of Roots of a Quadratic Equations\">Nature of Roots of a Quadratic Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#What_are_Quadratic_Equations\" title=\"What are Quadratic Equations?\">What are Quadratic Equations?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#How_are_Quadratic_equations_different_from_Quadratic_Polynomials\" title=\"How are Quadratic equations different from Quadratic Polynomials?\">How are Quadratic equations different from Quadratic Polynomials?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Methods_used_for_finding_roots_of_Quadratic_Equations\" title=\"Methods used for finding roots of Quadratic Equations\">Methods used for finding roots of Quadratic Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Graphical_Representation_of_Quadratic_Equations\" title=\"Graphical Representation of Quadratic Equations\">Graphical Representation of Quadratic Equations<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Type_of_Roots\" title=\"Type of Roots\">Type of Roots<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Nature_of_Roots\" title=\"Nature of Roots\">Nature of Roots<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/maths\/nature-of-roots\/#Solved_Examples_of_Quadratic_Functions\" title=\"Solved Examples of Quadratic Functions\">Solved Examples of Quadratic Functions<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Nature_of_Roots_of_a_Quadratic_Equations\"><\/span>Nature of Roots of a Quadratic Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Nature of Roots of a Quadratic Equations: A<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/nature-of-roots-of-quadratic-equation\/\"> quadratic equation<\/a> is an equation in which a variable appears in a power of two. The most common form of a quadratic equation is <strong>ax^2+bx+c=0<\/strong>, where a, b, and c are real numbers and x is the variable. The roots of a quadratic equation are the values of x that make the equation true. There are two roots of a quadratic equation, and they are both real numbers.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-126618 size-medium\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Nature-Of-Roots-300x212.jpg\" alt=\"Nature of Roots of a Quadratic Equation\" width=\"300\" height=\"212\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Nature-Of-Roots-300x212.jpg?v=1645815513 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Nature-Of-Roots.jpg?v=1645815513 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Quadratic_Equations\"><\/span><span style=\"font-size: 14pt;\">What are Quadratic Equations?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A quadratic equation is an equation in the form <strong>ax2 + bx + c = 0<\/strong>. The a, b, and c are constants, and x is the variable. The roots of a quadratic equation are the values of x that make the equation true.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_are_Quadratic_equations_different_from_Quadratic_Polynomials\"><\/span><span style=\"font-size: 14pt;\">How are Quadratic equations different from Quadratic Polynomials?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Quadratic equations are different from quadratic polynomials because an equation is a mathematical statement that two things are equal, while a polynomial is an expression consisting of one or more terms, each of which is a multiple of a power of x. In other words, a polynomial is an equation that can be written in the form<strong> ax^n+bx^n-1+cx^n-2+&#8230;+dx^2+ex+<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Methods_used_for_finding_roots_of_Quadratic_Equations\"><\/span><span style=\"font-size: 14pt;\">Methods used for finding roots of Quadratic Equations<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are various methods that can be used for finding the roots of a quadratic equation. The most common methods are the quadratic formula, factoring, and completing the square.<\/p>\n<p>The quadratic equation can be solved by using the quadratic formula, which is:<\/p>\n<p>The roots of the equation can also found by factoring the quadratic equation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Graphical_Representation_of_Quadratic_Equations\"><\/span><span style=\"font-size: 14pt;\">Graphical Representation of Quadratic Equations<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A quadratic equation is a mathematical equation that has the form: <strong>ax2 + bx + c = 0<\/strong><\/p>\n<p>The graph of a quadratic equation is a parabola. The equation can written in standard form, vertex form, or intercept form.<\/p>\n<p>The standard form of a quadratic equation is: <strong>ax2 + bx + c = 0<\/strong><\/p>\n<p>The vertex form of a quadratic equation is: <strong>x = \u2013b \u00b1<\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Type_of_Roots\"><\/span><span style=\"font-size: 14pt;\">Type of Roots<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>There are three types of roots in the English language:<\/p>\n<ul>\n<li>The root word is the base form of the word.<\/li>\n<li>The derivative word is a word that formed from the root word.<\/li>\n<li>The compound word is a word that formed from two or more root words.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Nature_of_Roots\"><\/span><span style=\"font-size: 14pt;\">Nature of Roots<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>One of the most interesting things about plants is their root systems. The roots of a plant are important for many reasons. They anchor the plant in the soil, they take in water and nutrients from the soil, and they help to distribute the plant&#8217;s water and nutrients throughout the plant.<\/p>\n<p>The roots of a plant are typically hidden from view, but they can seen when the soil turned over. The root system of a plant made up of two types of roots: the<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Solved_Examples_of_Quadratic_Functions\"><\/span><span style=\"font-size: 14pt;\">Solved Examples <\/span>of Quadratic Functions<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In mathematics, a quadratic function is a polynomial function in which the highest-degree term is a second-degree polynomial, such as x2 + 5x + 6. A function of the form f(x) = ax2 + bx + c, where a, b, and c are real numbers, and a \u2260 0, is a quadratic function. The graph of a quadratic function is a par<\/p>\n<p><strong><span style=\"font-size: 14pt;\">Facts and Theories<\/span><\/strong><\/p>\n<p>There are a number of different theories about how the world works. Some people believe that everything is random, and that there is no rhyme or reason to what happens. Others believe that there is a grand plan behind everything, and that everything happens for a specific reason. Between these two extremes are a number of other theories, including those that believe that there is some combination of chance and destiny at work, or that our actions have consequences that we cannot see.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nature of Roots of a Quadratic Equations Nature of Roots of a Quadratic Equations: A quadratic equation is an equation [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Nature of Roots of a Quadratic Equations","_yoast_wpseo_title":"Nature of Roots of a Quadratic Equations %%sep%% %%sitename%%","_yoast_wpseo_metadesc":"Learn Nature of Roots of a Quadratic Equations topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"study-materials\/maths\/nature-of-roots\/"},"categories":[13,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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