{"id":2303,"date":"2017-06-15T22:03:31","date_gmt":"2017-06-15T22:03:31","guid":{"rendered":"http:\/\/10.10.10.4:9191\/softlect\/?p=2303"},"modified":"2019-06-12T16:01:35","modified_gmt":"2019-06-12T16:01:35","slug":"quadratic-equation","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/quadratic-equation\/","title":{"rendered":"Quadratic Equation"},"content":{"rendered":"<p>Quadratic equation is a second order polynomial with 3 coefficients &#8211; <em>a<\/em>, <em>b<\/em>, <em>c<\/em>.<br \/>\nThe quadratic equation is given by:<br \/>\n<em>ax<\/em><sup>2 <\/sup>+<em> bx <\/em>+<em> c<\/em> = 0<br \/>\nThe solution to the quadratic equation is given by 2 numbers x<sub>1<\/sub> and x<sub>2<\/sub>.<br \/>\nWe can change the quadratic equation to the form of:<br \/>\n(<em>x <\/em>&#8211;<em> x<\/em><sub>1<\/sub>)(<em>x <\/em>&#8211;<em> x<\/em><sub>2<\/sub>) = 0<\/p>\n<h3>Quadratic Formula<\/h3>\n<p>The solution to the quadratic equation is given by the quadratic formula:<br \/>\n<img loading=\"lazy\" src=\"http:\/\/www.softlect.in\/imagesMaths\/quadratic_solution.gif\" alt=\"\" width=\"211\" height=\"49\" \/><br \/>\nThe expression inside the square root is called <em>discriminant<\/em> and is denoted by \u0394:<br \/>\n\u0394 = <em>b<\/em><sup>2<\/sup> &#8211; 4<em>ac<\/em><br \/>\nThe quadratic formula with discriminant notation:<br \/>\n<img loading=\"lazy\" src=\"http:\/\/www.softlect.in\/imagesMaths\/quadratic_solution2.gif\" alt=\"\" width=\"153\" height=\"50\" \/><br \/>\nThis expression is important because it can tell us about the solution:<\/p>\n<p>When \u0394&gt;0, there are 2 real roots x<sub>1<\/sub>=(-b+\u221a\u0394)\/(2a) and x<sub>2<\/sub>=(-b-\u221a\u0394)\/(2a)<sub>.<\/sub><br \/>\nWhen \u0394=0, there is one root x<sub>1<\/sub>=x<sub>2<\/sub>=-b\/(2a)<sub>.<\/sub><br \/>\nWhen \u0394&lt;0, there are no real roots, there are 2 complex roots x<sub>1<\/sub>=(-b+i\u221a-\u0394)\/(2a) and x<sub>2<\/sub>=(-b-i\u221a-\u0394)\/(2a)<sub>.<\/sub><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quadratic equation is a second order polynomial with 3 coefficients &#8211; a, b, c. The quadratic equation is given by: ax2 + bx + c = 0 The solution to&hellip; <\/p>\n","protected":false},"author":1,"featured_media":3125,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2303"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=2303"}],"version-history":[{"count":8,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2303\/revisions"}],"predecessor-version":[{"id":2385,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2303\/revisions\/2385"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3125"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=2303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=2303"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=2303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}