{"id":156110,"date":"2022-03-26T01:23:33","date_gmt":"2022-03-25T19:53:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/polynomial-equations-definition-formula-and-solving-polynomial-equations\/"},"modified":"2025-02-11T10:47:27","modified_gmt":"2025-02-11T05:17:27","slug":"polynomial-equations-definition-formula-and-solving-polynomial-equations","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/","title":{"rendered":"Polynomial Equations \u2013 Definition, Formula and Solving Polynomial Equations"},"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\/maths\/polynomial-equations\/#Polynomial_Equations_in_Detail\" title=\"Polynomial Equations in Detail\">Polynomial Equations in Detail<\/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\/maths\/polynomial-equations\/#What_is_a_Polynomial_Equation\" title=\"What is a Polynomial Equation?\">What is a Polynomial Equation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Degree_of_Polynomial\" title=\"Degree of Polynomial\">Degree of Polynomial<\/a><\/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\/maths\/polynomial-equations\/#Polynomial_Formula\" title=\"Polynomial Formula\">Polynomial Formula<\/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\/maths\/polynomial-equations\/#Types_of_Polynomial_Equation\" title=\"Types of Polynomial Equation\">Types of Polynomial Equation<\/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\/maths\/polynomial-equations\/#Monomial_Equation\" title=\"Monomial Equation:\">Monomial Equation:<\/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\/maths\/polynomial-equations\/#Binomial_Equations\" title=\"Binomial Equations:\">Binomial Equations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Trinomial_Equations\" title=\"Trinomial Equations:\">Trinomial Equations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Let_us_take_an_example\" title=\"Let us take an example:\">Let us take an example:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Quadratic_Polynomial_Equation\" title=\"Quadratic Polynomial Equation\">Quadratic Polynomial Equation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Solving_Polynomial_Equations\" title=\"Solving Polynomial Equations\">Solving Polynomial Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/#Application_of_Polynomial_Equations_in_Real_Life\" title=\"Application of Polynomial Equations in Real Life\">Application of Polynomial Equations in Real Life<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Polynomial_Equations_in_Detail\"><\/span>Polynomial Equations in Detail<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A <a href=\"https:\/\/en.wikipedia.org\/wiki\/Polynomial\" target=\"_blank\" rel=\"noopener\">polynomial<\/a> equation is an equation in which one or more terms are polynomials. A polynomial is an expression consisting of a finite number of terms, each of which is a product of a constant and one or more variables raised to a positive integer power. Polynomial Equations \u2013 Definition Formula and Solving Polynomial Equations.<\/p>\n<p>A polynomial equation can be solved by factoring the polynomial and solving the resulting equations.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156109 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-equations-definition-formula-and-solving-polynomial-equations.jpg\" alt=\"Polynomial Equations \u2013 Definition, Formula and Solving Polynomial Equations\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-equations-definition-formula-and-solving-polynomial-equations.jpg?v=1648238010 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-equations-definition-formula-and-solving-polynomial-equations-300x212.jpg?v=1648238010 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Polynomial_Equation\"><\/span>What is a Polynomial Equation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial equation is an equation in which at least one variable appears as a power of a nonzero constant. A polynomial equation always has a finite number of solutions.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Degree_of_Polynomial\"><\/span>Degree of Polynomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial is a mathematical expression consisting of one or more terms, each of which is an algebraic sum of a fixed number of monomials. A degree of a polynomial is the sum of the exponents of the variables in the polynomial.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Polynomial_Formula\"><\/span>Polynomial Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial is an expression that is made up of one or more terms, each of which is a multiple of a power of x. The polynomial expression is written in descending order from the highest power of x to the lowest.<\/p>\n<p>The degree of a polynomial is the highest power of x in the expression. The terms of a polynomial are separated by plus or minus signs, and parentheses may be used to group terms.<\/p>\n<p>A polynomial can be factored into a product of polynomials, each of which has a lower degree than the original polynomial.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Polynomial_Equation\"><\/span>Types of Polynomial Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial<\/a> equation is basically of four types;<\/p>\n<ol>\n<li>Monomial Equations<\/li>\n<li>Binomial Equations<\/li>\n<li>Trinomial or Cubic Equations<\/li>\n<li>Linear Polynomial Equations<\/li>\n<li>Quadratic Polynomial Equations<\/li>\n<li>Cubic Polynomial Equation<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Monomial_Equation\"><\/span>Monomial Equation:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An equation which has only one variable term is called a Monomial equation. This is also called a <strong>linear equation<\/strong>. It can be expressed in the algebraic form of;<\/p>\n<p><strong>ax + b = 0<\/strong><\/p>\n<p>For Example:<\/p>\n<ul>\n<li>4x + 1 = 0<\/li>\n<li>5y = 2<\/li>\n<li>8z \u2013 3 = 0<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Binomial_Equations\"><\/span>Binomial Equations:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An equation which has only two variable terms and is followed by one variable term is called a Binomial equation. This is also in the form of the <strong>quadratic equation<\/strong>. It can be expressed in the algebraic form of;<\/p>\n<p><strong>ax<sup>2 <\/sup>+ bx + c = 0<\/strong><\/p>\n<p>For Example:<\/p>\n<ul>\n<li>2x<sup>2 <\/sup>+ 5x + 20 = 0<\/li>\n<li>3x<sup>2 <\/sup>\u2013 4x + 12 = 0<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Trinomial_Equations\"><\/span><strong>Trinomial Equations:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An equation which has only three variable terms and is followed by two variable and one variable term is called a Trinomial equation. This is also called a <strong>cubic equation<\/strong>. In other words, a polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.<\/p>\n<p>Since the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.<\/p>\n<p>It is expressed as;<\/p>\n<p><strong>a<sub>0<\/sub> x<sup>3<\/sup> + a<sub>1<\/sub>x<sup>2<\/sup> + a<sub>2<\/sub>x + a<sub>3 <\/sub>= 0, a \u2260 <\/strong><strong>0<\/strong><\/p>\n<p>or<\/p>\n<p><strong>ax<sup>3 <\/sup>+ bx<sup>2<\/sup> + cx + d = 0<\/strong><\/p>\n<p><strong>For Example:<\/strong><\/p>\n<ul>\n<li>3x<sup>3 <\/sup>+ 12x<sup>2<\/sup> \u2013 8x \u2013 10 = 0<\/li>\n<li>9x<sup>3 <\/sup>+ 5x<sup>2<\/sup> \u2013 4x \u2013 2 = 0<\/li>\n<\/ul>\n<p>To get the value of x, we generally use, trial and error method, in which we start putting the value of x randomly, to get the given expression as 0. If for both sides of the polynomial equation, we get 0 ,then the value of x is considered as one of its roots. After that we can find the other two values of x.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Let_us_take_an_example\"><\/span>Let us take an example:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Problem:<\/strong> y<sup>3 <\/sup>\u2013 y<sup>2 <\/sup>+ y \u2013 1 = 0 is a cubic polynomial equation. Find the roots of it.<\/p>\n<p><strong>Solution: <\/strong>y<sup>3 <\/sup>\u2013 y<sup>2 <\/sup>+ y \u2013 1 = 0 is the given equation.<\/p>\n<p>By trial and error method, start putting the value of x.<\/p>\n<p>If y = -1, then,<\/p>\n<p>(-1)<sup>3 <\/sup>\u2013 (-1)<sup>2<\/sup> -1 + 1 = 0<\/p>\n<p>-1 \u2013 1 \u2013 1 \u2013 1 = 0<\/p>\n<p>-4 \u2260 0<\/p>\n<p>If y = 1, then,<\/p>\n<p>1<sup>3 <\/sup>\u2013 1<sup>2 <\/sup>+ 1 \u2013 1 = 0<\/p>\n<p>0 = 0<\/p>\n<p>Therefore, one of the roots is 1.<\/p>\n<p>y = 1<\/p>\n<p>(y \u2013 1) is one of the factors.<\/p>\n<p>Now dividing the given equation with (y \u2013 1), we get,<\/p>\n<p>(y \u2013 1) (y<sup>2 <\/sup>+  1) = 0<\/p>\n<p>Therefore, the roots are y = 1 which is a real number and y<sup>2 <\/sup>+ 1 gives complex numbers or imaginary numbers.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Quadratic_Polynomial_Equation\"><\/span>Quadratic Polynomial Equation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A polynomial equation which has a degree as two is called a quadratic equation. The expression for the quadratic equation is:<\/p>\n<p><strong>ax<sup>2 <\/sup>+ bx + c = 0 ; a \u2260 0<\/strong><\/p>\n<p>Here, a,b, and c are real numbers. The roots of quadratic equations will be two values for the variable x<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solving_Polynomial_Equations\"><\/span>Solving Polynomial Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial equation is an equation that contains a polynomial. A polynomial is an expression that contains one or more terms, each of which is a product of a constant and a variable raised to a nonnegative integer power.<\/p>\n<p>A polynomial equation can be solved using the Quadratic Formula.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Application_of_Polynomial_Equations_in_Real_Life\"><\/span>Application of Polynomial Equations in Real Life<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Polynomial equations can be used in a number of different ways in the real world. One way is to find the curve of a graph that best fits the data points. This is often done with polynomial regression. Polynomial equations can also be used to solve problems in physics and engineering. For example, they can be used to find the displacement of an object at a certain time or the force on an object at a certain point in space.<\/p>\n<p>Polynomial Equations \u2013 Definition Formula and Solving Polynomial Equations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Polynomial Equations in Detail A polynomial equation is an equation in which one or more terms are polynomials. A polynomial [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Polynomial Equations \u2013 Definition Formula and Solving Polynomial Equations","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Polynomial Equations \u2013 Definition Formula and Solving Polynomial Equations explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/polynomial-equations\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Polynomial Equations \u2013 Definition, Formula and Solving Polynomial Equations - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Polynomial Equations \u2013 Definition Formula and Solving Polynomial Equations explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polynomial Equations \u2013 Definition, Formula and Solving Polynomial Equations - 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