Which are the solutions of x^2=19x+1?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the quadratic equation (x^2 = 19x + 1), we first rearrange it into standard form. Standard form for a quadratic equation is given by:<\/p>\n\n\n\n [ In our case, we can rewrite the equation as:<\/p>\n\n\n\n [ Here, (a = 1), (b = -19), and (c = -1). To find the solutions to this quadratic equation, we will use the quadratic formula:<\/p>\n\n\n\n [ Substituting the values of (a), (b), and (c) into the formula, we first calculate the discriminant ((b^2 – 4ac)):<\/p>\n\n\n\n [ [ [ Now that we have the discriminant, we can substitute back into the quadratic formula:<\/p>\n\n\n\n [ Next, we calculate (\\sqrt{365}). Approximating this value:<\/p>\n\n\n\n [ Now we substitute this approximation back into our formula:<\/p>\n\n\n\n [ This yields two possible solutions:<\/p>\n\n\n\n Therefore, the solutions to the equation (x^2 = 19x + 1) are approximately:<\/p>\n\n\n\n [ In conclusion, the solutions to the quadratic equation are (x \\approx 19.05) and (x \\approx -0.05).<\/p>\n","protected":false},"excerpt":{"rendered":" Which are the solutions of x^2=19x+1? The Correct Answer and Explanation is: To solve the quadratic equation (x^2 = 19x + 1), we first rearrange it into standard form. Standard form for a quadratic equation is given by: [ax^2 + bx + c = 0] In our case, we can rewrite the equation as: [x^2 […]<\/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-161681","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161681","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=161681"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161681\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
ax^2 + bx + c = 0
]<\/p>\n\n\n\n
x^2 – 19x – 1 = 0
]<\/p>\n\n\n\n
x = \\frac{{-b \\pm \\sqrt{{b^2 – 4ac}}}}{{2a}}
]<\/p>\n\n\n\n\n
b^2 = (-19)^2 = 361
]<\/p>\n\n\n\n\n
4ac = 4 \\cdot 1 \\cdot (-1) = -4
]<\/p>\n\n\n\n\n
b^2 – 4ac = 361 – (-4) = 361 + 4 = 365
]<\/p>\n\n\n\n
x = \\frac{{-(-19) \\pm \\sqrt{365}}}{{2 \\cdot 1}} = \\frac{{19 \\pm \\sqrt{365}}}{2}
]<\/p>\n\n\n\n
\\sqrt{365} \\approx 19.1
]<\/p>\n\n\n\n
x = \\frac{{19 \\pm 19.1}}{2}
]<\/p>\n\n\n\n\n
x_1 \\approx 19.05 \\quad \\text{and} \\quad x_2 \\approx -0.05
]<\/p>\n\n\n\n