If 5x + x2 > 100, then x is not
10
08
07
09<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The given inequality is:<\/p>\n\n\n\n [ We need to determine for which values of ( x ), this inequality does not hold. In other words, we need to find the values of ( x ) that do not<\/strong> satisfy this inequality.<\/p>\n\n\n\n Rearrange the given inequality:<\/p>\n\n\n\n [ This is a quadratic inequality of the form ( ax^2 + bx + c > 0 ), where ( a = 1 ), ( b = 5 ), and ( c = -100 ).<\/p>\n\n\n\n We now solve the related quadratic equation:<\/p>\n\n\n\n [ To solve for ( x ), we can use the quadratic formula:<\/p>\n\n\n\n [ Substitute ( a = 1 ), ( b = 5 ), and ( c = -100 ) into the quadratic formula:<\/p>\n\n\n\n [ The square root of 425 is approximately 20.615, so:<\/p>\n\n\n\n [ This gives two solutions:<\/p>\n\n\n\n [ Thus, the roots of the equation are approximately ( x_1 \\approx 7.81 ) and ( x_2 \\approx -12.81 ).<\/p>\n\n\n\n Now that we have the roots, we can analyze the inequality ( x^2 + 5x – 100 > 0 ). The quadratic expression will be greater than 0 outside the interval defined by the roots. Specifically, the inequality will hold for:<\/p>\n\n\n\n [ Therefore, the inequality is not satisfied<\/strong> for values of ( x ) in the interval ( -12.81 < x < 7.81 ).<\/p>\n\n\n\n The options provided are:<\/p>\n\n\n\n Now, we check these values against the interval where the inequality does not hold (i.e., between ( -12.81 ) and ( 7.81 )):<\/p>\n\n\n\n The value of ( x ) that does not<\/strong> satisfy the inequality ( 5x + x^2 > 100 ) is ( 07 ).<\/p>\n\n\n\n Therefore, the correct answer is ( \\boxed{07} ).<\/p>\n","protected":false},"excerpt":{"rendered":" If 5x + x2 > 100, then x is not10080709 The correct answer and explanation is : The given inequality is: [5x + x^2 > 100] We need to determine for which values of ( x ), this inequality does not hold. In other words, we need to find the values of ( x ) […]<\/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-197713","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197713","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=197713"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197713\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=197713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=197713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=197713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
5x + x^2 > 100
]<\/p>\n\n\n\nStep 1: Rewrite the inequality<\/h3>\n\n\n\n
x^2 + 5x – 100 > 0
]<\/p>\n\n\n\nStep 2: Solve the corresponding quadratic equation<\/h3>\n\n\n\n
x^2 + 5x – 100 = 0
]<\/p>\n\n\n\n
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
]<\/p>\n\n\n\n
x = \\frac{-5 \\pm \\sqrt{5^2 – 4(1)(-100)}}{2(1)}
]
[
x = \\frac{-5 \\pm \\sqrt{25 + 400}}{2}
]
[
x = \\frac{-5 \\pm \\sqrt{425}}{2}
]<\/p>\n\n\n\n
x = \\frac{-5 \\pm 20.615}{2}
]<\/p>\n\n\n\n
x_1 = \\frac{-5 + 20.615}{2} \\approx 7.81
]
[
x_2 = \\frac{-5 – 20.615}{2} \\approx -12.81
]<\/p>\n\n\n\nStep 3: Analyze the inequality<\/h3>\n\n\n\n
x < -12.81 \\quad \\text{or} \\quad x > 7.81
]<\/p>\n\n\n\nStep 4: Check the given options<\/h3>\n\n\n\n
\n
\n
Conclusion<\/h3>\n\n\n\n