What is the solution set of x2 + 5x + 1 = 0?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve the quadratic equation ( x^2 + 5x + 1 = 0 ), we can use the quadratic formula. The general form of a quadratic equation is:<\/p>\n\n\n\n [ where ( a ), ( b ), and ( c ) are constants. In this case, we have:<\/p>\n\n\n\n The quadratic formula is:<\/p>\n\n\n\n [ [ [ [ [ The solution set of the quadratic equation ( x^2 + 5x + 1 = 0 ) is:<\/p>\n\n\n\n [ These are the two real and distinct solutions to the equation.<\/p>\n\n\n\n This is a quadratic equation because the highest power of ( x ) is 2, which means it has at most two solutions. In this case, the discriminant ( b^2 – 4ac = 21 ) is positive, which indicates that there are two distinct real solutions.<\/p>\n\n\n\n The solutions come from the quadratic formula, which ensures that every quadratic equation has a solution, either real or complex. In this example, the solutions are real because the discriminant is positive. The expression ( \\sqrt{21} ) is irrational, so the solutions are also irrational numbers.<\/p>\n\n\n\n Thus, the solution set is composed of two irrational numbers, representing the values of ( x ) that satisfy the original equation.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the solution set of x2 + 5x + 1 = 0? The Correct Answer and Explanation is : To solve the quadratic equation ( x^2 + 5x + 1 = 0 ), we can use the quadratic formula. The general form of a quadratic equation is: [ax^2 + bx + c = 0] […]<\/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-163120","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163120","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=163120"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163120\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
ax^2 + bx + c = 0
]<\/p>\n\n\n\n\n
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
]<\/p>\n\n\n\nStep-by-Step Solution:<\/h3>\n\n\n\n
\n
x = \\frac{-5 \\pm \\sqrt{5^2 – 4(1)(1)}}{2(1)}
]<\/p>\n\n\n\n\n
x = \\frac{-5 \\pm \\sqrt{25 – 4}}{2}
]<\/p>\n\n\n\n
x = \\frac{-5 \\pm \\sqrt{21}}{2}
]<\/p>\n\n\n\n\n
x = \\frac{-5 + \\sqrt{21}}{2} \\quad \\text{or} \\quad x = \\frac{-5 – \\sqrt{21}}{2}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
x = \\frac{-5 + \\sqrt{21}}{2} \\quad \\text{or} \\quad x = \\frac{-5 – \\sqrt{21}}{2}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n