{"id":1671,"date":"2014-12-23T10:21:42","date_gmt":"2014-12-23T10:21:42","guid":{"rendered":"https:\/\/myassignmenthelp.com\/blog\/?p=1671"},"modified":"2026-04-30T06:02:47","modified_gmt":"2026-04-30T06:02:47","slug":"how-to-solve-cubic-equation-step-by-step","status":"publish","type":"post","link":"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/","title":{"rendered":"How to Solve a Cubic Equation : ax3+ bx2+cx+d= 0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69f9529d73e53\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"ez-toc-cssicon\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69f9529d73e53\" checked aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#Learn_To_Solve_Cubic_Equations\" >Learn To Solve Cubic 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:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#Ways_of_Solving_Cubic_Equation\" >Ways of Solving Cubic 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:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#Solving_Cubic_Equations_with_the_Help_of_Factor_Theorem\" >Solving Cubic Equations with the Help of Factor Theorem<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#i\" >&nbsp;<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#ANOTHER_EXAMPLE\" >ANOTHER EXAMPLE:<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#You_can_simply_try_x_%E2%80%93_1_after_putting_the_value_of_x_you_will_get\" >You can simply try x = \u2013 1, after putting the value of x, you will get,<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/#How_MyAssignmenthelpcom_can_help_students_in_maths_assignment\" >How MyAssignmenthelp.com can help students in maths assignment<\/a><\/li><\/ul><\/nav><\/div>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Learn_To_Solve_Cubic_Equations\"><\/span>Learn To Solve Cubic Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In mathematical terms, all cubic equations have either one root or three real roots. The general cubic equation is,<\/p>\n\n\n\n<p><strong>ax<sup>3<\/sup>+ bx<sup>2<\/sup>+ cx+d= 0<\/strong><\/p>\n\n\n\n<p>The coefficients of a, b, c, and d are real or complex numbers with a not equals to zero (a \u2260 0). It must have the term <strong>x<sup>3<\/sup><\/strong> &nbsp; in it, or else it will not be a cubic equation. But any or all of b, c and d can be zero.<\/p>\n\n\n\n<p>The examples of cubic equations are,<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong><span style=\"color: #ff0000;\">3<\/span>x<sup>3<\/sup>+ 3x<sup>2<\/sup><\/strong> <strong>+ x\u2013 b=0<\/strong><\/li>\n\n\n\n<li><strong><span style=\"color: #ff0000;\">4<\/span>x<sup>3<\/sup>+ 57=0<\/strong><\/li>\n\n\n\n<li><strong><span style=\"color: #ff0000;\">1<\/span>.x<sup>3<\/sup>+ 9x=0&nbsp; &nbsp;or x<sup>3<\/sup>+ 9x=0<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Note: &nbsp;a or the coefficient before x<sup>3 <\/sup>(<span style=\"color: #ff0000;\">that is highlighted<\/span>) is not equal to 0.The highest power of variable x in the equation is 3.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ways_of_Solving_Cubic_Equation\"><\/span>Ways of Solving Cubic Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Unlike quadratic equation which may have no real solution; a cubic equation solver always has at least one real root. The prior strategy of solving a cubic equation is to reduce it to a quadratic equation, and then solve the quadratic by usual means, either by factorizing or using a formula.<\/p>\n\n\n\n<p>Always try to find the solution of cubic equations with the help of the general equation,<\/p>\n\n\n\n<p><strong>ax<sup>3<\/sup>+ bx<sup>2<\/sup>+ cx+d= 0<\/strong><\/p>\n\n\n\n<p>A cubic equation should, therefore, must be re-arranged into its standard form,<\/p>\n\n\n\n<p>For example,<\/p>\n\n\n\n<p><strong><span style=\"font-size: 10.5pt;\">x<sup>2<\/sup>+ 4x-1 =&nbsp; 6\/x<\/span><\/strong><\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 1<\/strong><\/span><\/p>\n\n\n\n<p>You can see the equation is not written in standard form, you need to multiply the \u2018x\u2019 to eliminate the fraction and get cubic equation, after doing so, you will end up with<\/p>\n\n\n\n<p><strong>x (<\/strong><strong><span style=\"font-size: 10.5pt;\">x<sup>2<\/sup>+ 4x-1) = 6<\/span> <\/strong><\/p>\n\n\n\n<p><strong>x<sup>3<\/sup>+ 4x<sup>2<\/sup>\u2013 x = 6<\/strong><\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 2<\/strong><\/span><\/p>\n\n\n\n<p>Then you subtract 6 from both sides in order to get \u20180\u2019 on the right side, so you will come up,<\/p>\n\n\n\n<p><strong>x<sup>3<\/sup>+ 4x<sup>2<\/sup>\u2013 x- 6 = 0<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solving_Cubic_Equations_with_the_Help_of_Factor_Theorem\"><\/span><strong><span style=\"font-weight: normal;\">Solving Cubic Equations with the Help of Factor Theorem<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>What is factor theorem? If you divide a polynomial p(x) by a factor x \u2013 a of that polynomial, then, you will end up with zero as the remainder,<\/p>\n\n\n\n<p><strong>p(x) = (x \u2013 a) q(x) + r(x)<\/strong><\/p>\n\n\n\n<p>If <strong>x \u2013 a<\/strong> is indeed a factor of p(x), then the remainder after division by <strong>x \u2013 a<\/strong> will be zero.<\/p>\n\n\n\n<p><strong>p(x) = (x \u2013 a)q (x)<\/strong><\/p>\n\n\n\n<p>Here is a problem,<\/p>\n\n\n\n<p><strong>x<sup>3<\/sup>\u2013 5x<sup>2<\/sup>\u2013 2x+24 = 0<\/strong><\/p>\n\n\n\n<p>With&nbsp;<strong>x= \u2013 2&nbsp;<\/strong>a solution.<\/p>\n\n\n\n<p>Factor theorem says that if&nbsp;<strong>&nbsp;x = \u2013 2<\/strong>&nbsp;is a solution of this equation, then&nbsp;<strong>x+2<\/strong>&nbsp;is a factor of this whole expression. So,<\/p>\n\n\n\n<p><strong>x<sup>3<\/sup>\u2013 5x<sup>2<\/sup>\u2013 2x+24 = 0<\/strong><\/p>\n\n\n\n<p>can be written in the form,<\/p>\n\n\n\n<p><strong>(x+2)( x<sup>2<\/sup>+ ax+b)=0&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p>Where&nbsp;<em>a<\/em>&nbsp;and&nbsp;<em>b<\/em>&nbsp;are numbers,<\/p>\n\n\n\n<p>You need to find out what are the values of&nbsp;<em>a<\/em>&nbsp;and&nbsp;<em>b<\/em> here by using synthetic division.<strong><span style=\"font-family: SimSun;\">&nbsp;<\/span><\/strong><\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 1<\/strong><\/span><\/p>\n\n\n\n<p>First, you need to look at the coefficients of the original cubic equation, which are&nbsp;<strong>1, -5, -2<\/strong>&nbsp;and&nbsp;<strong>24.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"356\" height=\"184\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/a.png\" alt=\"Solving Cubic Equations with the Help of Factor Theorem\" class=\"wp-image-9741\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/a.png 356w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/a-350x181.png 350w\" sizes=\"auto, (max-width: 356px) 85vw, 356px\" \/><\/figure><\/div>\n\n\n<p>To the right of the vertical you need to write down the known root,<strong>&nbsp;x = -2<\/strong><\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 2<\/strong><\/span><\/p>\n\n\n\n<p>Now multiply number (1) that just brought down, by the known root&nbsp;<strong>-2<\/strong>, as a result is&nbsp;<strong>-2<\/strong>, you mention the result in the other line, like<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"205\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/b.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9742\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/b.png 413w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/b-350x174.png 350w\" sizes=\"auto, (max-width: 413px) 85vw, 413px\" \/><\/figure><\/div>\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 3<\/strong><\/span><\/p>\n\n\n\n<p>The numbers in the second column are added, so giving us,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"245\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/c.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9743\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/c.png 402w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/c-328x200.png 328w\" sizes=\"auto, (max-width: 402px) 85vw, 402px\" \/><\/figure><\/div>\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 4<\/strong><\/span><\/p>\n\n\n\n<p>Then recently written number<strong>&nbsp;7<\/strong>&nbsp;is multiplied by the known root,&nbsp;<strong>\u2013 2<\/strong>,<\/p>\n\n\n\n<p>As 14 comes as a result, you need to write it down on the second row over the line,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"427\" height=\"232\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/d.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9744\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/d.png 427w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/d-350x190.png 350w\" sizes=\"auto, (max-width: 427px) 85vw, 427px\" \/><\/figure><\/div>\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 5<\/strong><\/span><\/p>\n\n\n\n<p>Like previously the numbers in this column added,&nbsp;<strong>(14 \u2013 2 = 12)<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"233\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/e.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9745\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/e.png 412w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/e-350x198.png 350w\" sizes=\"auto, (max-width: 412px) 85vw, 412px\" \/><\/figure><\/div>\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 6<\/strong><\/span><\/p>\n\n\n\n<p>And you need to go on with the process,&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"i\"><\/span><strong> <\/strong><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"219\" class=\"size-full wp-image-9746 aligncenter\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/f.png\" alt=\"Solve Cubic Equations\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/f.png 385w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/f-350x200.png 350w\" sizes=\"auto, (max-width: 385px) 85vw, 385px\" \/><strong>&nbsp;<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 7<\/strong><\/span><\/p>\n\n\n\n<p>When you have zero at the bottom row, it gives the confirmation that <strong>x = \u2013 2<\/strong> is a root of the original cubic. At this stage, you got the first three numbers in the bottom row as the coefficients in the quadratic,<\/p>\n\n\n\n<p>x<sup>2<\/sup>\u2013 7x+12<\/p>\n\n\n\n<p>Hence, you reduced your cubic to,<\/p>\n\n\n\n<p>(x+2)(x<sup>2<\/sup>&nbsp;\u2013 7x + 12) =0<\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 8<\/strong><\/span><\/p>\n\n\n\n<p>After applying the quadratic term, the equation comes like this,<\/p>\n\n\n\n<p>(x +2) (x \u2013 3) (x \u2013 4) = 0<\/p>\n\n\n\n<p>Resulting, you get the solution as&nbsp;<strong>x = -2<\/strong>&nbsp;or&nbsp;<strong>3&nbsp;<\/strong>or&nbsp;<strong>4<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ANOTHER_EXAMPLE\"><\/span><strong><span style=\"font-weight: normal;\">ANOTHER EXAMPLE:<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The equation is,<\/p>\n\n\n\n<p>x<sup>3<\/sup>\u2013 7x-6=0<\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 1<\/strong><\/span><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"You_can_simply_try_x_%E2%80%93_1_after_putting_the_value_of_x_you_will_get\"><\/span>You can simply try x = <span lang=\"ZH-CN\">\u2013<\/span> 1, after putting the value of x, you will get,<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>(-1)<sup>3 \u2013 <\/sup>7(-1) -6<\/p>\n\n\n\n<p>The result comes as zero, so it is proved that x +1 is a factor and the cubic can be written in the form,<\/p>\n\n\n\n<p>(x+1)(x<sup>2<\/sup>+ax+b)= 0<\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 2<\/strong><\/span><\/p>\n\n\n\n<p>After applying the synthetic division, like above example, you will take the coefficients of the original cubic equation, which are&nbsp;<strong>1, 0, -7<\/strong>&nbsp;and&nbsp;<strong>-6<\/strong>, you need to write down the know root x = -1 to the right of the vertical line, giving us,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"409\" height=\"232\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/g.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9747\" style=\"width:409px;height:auto\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/g.png 409w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/g-350x200.png 350w\" sizes=\"auto, (max-width: 409px) 85vw, 409px\" \/><\/figure><\/div>\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 3<\/strong><\/span><\/p>\n\n\n\n<p>Multiply the brought down number&nbsp;<strong>1<\/strong>&nbsp;by the known root&nbsp;<strong>x = -1<\/strong>, and put down the result&nbsp;<strong>(-1)<\/strong> at the second row, like this, &nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><img loading=\"lazy\" decoding=\"async\" width=\"476\" height=\"247\" class=\"aligncenter size-full wp-image-9748\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/h.png\" alt=\"Solve Cubic Equations\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/h.png 476w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/h-350x182.png 350w\" sizes=\"auto, (max-width: 476px) 85vw, 476px\" \/><\/h4>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 4<\/strong><\/span><\/p>\n\n\n\n<p>The numbers of the second column are added to the first column, giving us,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"443\" height=\"256\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/I.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9749\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/I.png 443w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/I-346x200.png 346w\" sizes=\"auto, (max-width: 443px) 85vw, 443px\" \/><\/figure><\/div>\n\n\n<p>And continue the process adding numbers in this column, until you find<strong>&nbsp;\u20180\u2019<\/strong>&nbsp;as a result,<\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 5<\/strong><\/span><\/p>\n\n\n\n<p>As you add more numbers to the second column by following the synthetic division process, you will come up with,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"448\" height=\"211\" src=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/J.png\" alt=\"Solve Cubic Equations\" class=\"wp-image-9750\" srcset=\"https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/J.png 448w, https:\/\/myassignmenthelp.com\/blog\/wp-content\/uploads\/2014\/12\/J-350x165.png 350w\" sizes=\"auto, (max-width: 448px) 85vw, 448px\" \/><\/figure><\/div>\n\n\n<p>When you come up with zero, it is confirmation that&nbsp;<strong>x = -1<\/strong>,<\/p>\n\n\n\n<p>Hence, you get the coefficients in the quadratic as the first three numbers in the bottom row, so the quadratic is, <strong>x<sup>2&nbsp;<\/sup>-x \u2013 6<\/strong><\/p>\n\n\n\n<p><span style=\"color: #ff0000;\"><strong>Step 6<\/strong><\/span><\/p>\n\n\n\n<p>Hence, the cubic reduced to quadratic,<\/p>\n\n\n\n<p><strong>(x+1)(x<sup>2<\/sup>-x- 6) =0<\/strong><\/p>\n\n\n\n<p>The factorized result is,<\/p>\n\n\n\n<p><strong>(x +1)(x \u2013 3)(x + 2) = 0<\/strong><\/p>\n\n\n\n<p>The three solutions or roots to the cubic equation are&nbsp;<strong>x = -2, -1&nbsp;<\/strong>or<strong>&nbsp;3<\/strong><\/p>\n\n\n\n<p>Are you looking for Assignment Help with 100% accuracy? If you need <strong><a href=\"https:\/\/myassignmenthelp.com\/homework\/do-my-math-homework.html\" data-type=\"link\" data-id=\"https:\/\/myassignmenthelp.com\/homework\/do-my-math-homework.html\">professional do my math homework<\/a><\/strong> support, MyAssignmenthelp.com has 3000+ <strong><a href=\"https:\/\/myassignmenthelp.com\/homework\/\">expert homework helper<\/a><\/strong> ready to help with your Assignment Writing, whether it\u2019s algebra, cubic equations, or <strong><a href=\"https:\/\/myassignmenthelp.com\/calculus-assignment-help.html\">advanced calculus assistance<\/a><\/strong>. They also provide 24\u00d77 online support to guide you through complex mathematical concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"How_MyAssignmenthelpcom_can_help_students_in_maths_assignment\"><\/span>How MyAssignmenthelp.com can help students in maths assignment<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>MyAssignmenthelp.com&nbsp;has carefully evaluated and assembled a highly-skilled team of in-house experts who are capable of giving the finest maths\u2002homework help&nbsp;you deserve. Your paper will be professionally written by experienced writers. <a href=\"https:\/\/myassignmenthelp.com\/experts\/\">Assignment experts <\/a>make sure that there are no traces of plagiarism in your content, and they only deliver genuine work within the given time limit. If you think sample assignments can help you with your&nbsp;assignment, MyAssignmenthelp.com offers free samples. Our customer support agents can guide you on how to get free assignment quotes and <a href=\"https:\/\/myassignmenthelp.com\/Home\/\">place your orders<\/a>. Get help with <a href=\"https:\/\/myassignmenthelp.com\/spss-assignment-help.html\">SPSS analysis<\/a> for better statistical reports.<\/p>\n\n\n\n<p><strong>Related Blog:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Math\u2019s !!! How to crack???<\/li>\n\n\n\n<li>How to Solve the Math Equation: A+B+B+B+80+90=100 Logically<\/li>\n\n\n\n<li>How to Solve a Variable Equation<\/li>\n\n\n\n<li>How to Solve Linear Equations<\/li>\n<\/ul>\n\n\n\n<p><strong>Glossary:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Real Root :<\/strong> A real number x will be called a solution or a root if it satisfies the equation.<\/li>\n\n\n\n<li><strong>Polynomials:<\/strong> An expression consisting of variables, constants and operator functions like (-) (+) (*) (\/). Ex: x<sup>2<\/sup> &#8211; 4x +7<strong>&nbsp;<\/strong><\/li>\n\n\n\n<li><strong>Variable: <\/strong>Any quantity that changes in a mathematical equation is called a variable. Commonly, we use an alphabet to represent a <strong>variable<\/strong>. <strong>x<\/strong> is the variable in the above equation.<\/li>\n\n\n\n<li><strong>Factor theorem<\/strong>: It is a theorem which links factors and zeros of polynomials.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Learn To Solve Cubic Equations In mathematical terms, all cubic equations have either one root or three real roots. The general cubic equation is, ax3+ bx2+ cx+d= 0 The coefficients of a, b, c, and d are real or complex numbers with a not equals to zero (a \u2260 0). It must have the term &hellip; <a href=\"https:\/\/myassignmenthelp.com\/blog\/how-to-solve-cubic-equation-step-by-step\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;How to Solve a Cubic Equation : ax3+ bx2+cx+d= 0&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":29233,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3100],"tags":[634,631,632,633,120],"class_list":["post-1671","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-other","tag-cubic-equations","tag-math-equation-editor","tag-math-equation-solver","tag-math-equation-writer","tag-maths-assignments-help"],"_links":{"self":[{"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/posts\/1671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/comments?post=1671"}],"version-history":[{"count":18,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/posts\/1671\/revisions"}],"predecessor-version":[{"id":36451,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/posts\/1671\/revisions\/36451"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/media\/29233"}],"wp:attachment":[{"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/media?parent=1671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/categories?post=1671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/myassignmenthelp.com\/blog\/wp-json\/wp\/v2\/tags?post=1671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}