To solve the quadratic equation 3×2+5x+1=03x^2 + 5x + 1 = 03×2+5x+1=0 using the quadratic formula, we will first recall the general quadratic formula:x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n
Here, the coefficients from the equation 3×2+5x+1=03x^2 + 5x + 1 = 03×2+5x+1=0 are:<\/p>\n\n\n\n
- \n
- a=3a = 3a=3<\/li>\n\n\n\n
- b=5b = 5b=5<\/li>\n\n\n\n
- c=1c = 1c=1<\/li>\n<\/ul>\n\n\n\n
Step 1: Identify the coefficients<\/h3>\n\n\n\n
From the given quadratic equation:<\/p>\n\n\n\n
- \n
- a=3a = 3a=3<\/li>\n\n\n\n
- b=5b = 5b=5<\/li>\n\n\n\n
- c=1c = 1c=1<\/li>\n<\/ul>\n\n\n\n
Step 2: Substitute into the quadratic formula<\/h3>\n\n\n\n
Substitute the values of aaa, bbb, and ccc into the quadratic formula:x=\u22125\u00b152\u22124(3)(1)2(3)x = \\frac{-5 \\pm \\sqrt{5^2 – 4(3)(1)}}{2(3)}x=2(3)\u22125\u00b152\u22124(3)(1)\u200b\u200b<\/p>\n\n\n\n
Step 3: Simplify the discriminant<\/h3>\n\n\n\n
First, calculate the discriminant (the part under the square root):b2\u22124ac=52\u22124(3)(1)=25\u221212=13b^2 – 4ac = 5^2 – 4(3)(1) = 25 – 12 = 13b2\u22124ac=52\u22124(3)(1)=25\u221212=13<\/p>\n\n\n\n
Now, substitute the discriminant value back into the formula:x=\u22125\u00b1136x = \\frac{-5 \\pm \\sqrt{13}}{6}x=6\u22125\u00b113\u200b\u200b<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
We now have two possible solutions for xxx because of the \u00b1\\pm\u00b1 sign:x=\u22125+136orx=\u22125\u2212136x = \\frac{-5 + \\sqrt{13}}{6} \\quad \\text{or} \\quad x = \\frac{-5 – \\sqrt{13}}{6}x=6\u22125+13\u200b\u200borx=6\u22125\u221213\u200b\u200b<\/p>\n\n\n\n
Step 5: Approximate the solutions<\/h3>\n\n\n\n
For practical purposes, we can approximate the square root of 13:13\u22483.6055\\sqrt{13} \\approx 3.605513\u200b\u22483.6055<\/p>\n\n\n\n
Now, substitute this value into the two solutions:<\/p>\n\n\n\n
- \n
- x=\u22125+3.60556=\u22121.39456\u2248\u22120.2324x = \\frac{-5 + 3.6055}{6} = \\frac{-1.3945}{6} \\approx -0.2324x=6\u22125+3.6055\u200b=6\u22121.3945\u200b\u2248\u22120.2324<\/li>\n\n\n\n
- x=\u22125\u22123.60556=\u22128.60556\u2248\u22121.4342x = \\frac{-5 – 3.6055}{6} = \\frac{-8.6055}{6} \\approx -1.4342x=6\u22125\u22123.6055\u200b=6\u22128.6055\u200b\u2248\u22121.4342<\/li>\n<\/ol>\n\n\n\n
Final Solutions:<\/h3>\n\n\n\n
The solutions to the quadratic equation 3×2+5x+1=03x^2 + 5x + 1 = 03×2+5x+1=0 are approximately:x\u2248\u22120.2324orx\u2248\u22121.4342x \\approx -0.2324 \\quad \\text{or} \\quad x \\approx -1.4342x\u2248\u22120.2324orx\u2248\u22121.4342<\/p>\n\n\n\n
These are the two real roots of the equation.<\/p>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"Solve this quadratic equation using the quadratic formula. 3×2 + 5x + 1 = 0 The Correct Answer and Explanation is: To solve the quadratic equation 3×2+5x+1=03x^2 + 5x + 1 = 03×2+5x+1=0 using the quadratic formula, we will first recall the general quadratic formula:x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b Here, the coefficients from […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-260624","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/260624","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=260624"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/260624\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=260624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=260624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=260624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}