{"id":160477,"date":"2023-09-28T13:45:29","date_gmt":"2023-09-28T08:15:29","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160477"},"modified":"2023-09-28T13:45:30","modified_gmt":"2023-09-28T08:15:30","slug":"consider-%f0%9d%91%9d%f0%9d%91%a0-%f0%9d%91%a03-%f0%9d%91%8e2%f0%9d%91%a02-%f0%9d%91%8e1%f0%9d%91%a0-%f0%9d%91%8e0-with-all-real-coefficients-it-is-known-that-its-derivative-%f0%9d%91%9d","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-%f0%9d%91%9d%f0%9d%91%a0-%f0%9d%91%a03-%f0%9d%91%8e2%f0%9d%91%a02-%f0%9d%91%8e1%f0%9d%91%a0-%f0%9d%91%8e0-with-all-real-coefficients-it-is-known-that-its-derivative-%f0%9d%91%9d\/","title":{"rendered":"Consider \ud835\udc5d(\ud835\udc60) = \ud835\udc603 + \ud835\udc4e2\ud835\udc602 + \ud835\udc4e1\ud835\udc60 + \ud835\udc4e0 with all real coefficients It is known that its derivative \ud835\udc5d\u2032(\ud835\udc60) has no real roots"},"content":{"rendered":"\n<p>Q. Consider \ud835\udc5d(\ud835\udc60) = \ud835\udc60<sup>3<\/sup> + \ud835\udc4e<sub>2<\/sub>\ud835\udc60<sup>2<\/sup> + \ud835\udc4e<sub>1<\/sub>\ud835\udc60 + \ud835\udc4e<sub>0<\/sub> with all real coefficients. It is known that its derivative \ud835\udc5d\u2032(\ud835\udc60) has no real roots. The number of real roots of \ud835\udc5d(\ud835\udc60) is<\/p>\n\n\n\n<p>(A) 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (C) 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (D) 3<\/p>\n\n\n\n<p>Ans: 1<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Given p(s) = s3 + a2\u00a0s2 + a1s + a0 <\/p>\n\n\n\n<p>p'(s) = 3s2 + 2a2s + a1 <\/p>\n\n\n\n<p>Also given that p'(s) has no real roots, therefore, we can write: <\/p>\n\n\n\n<p>n &#8211; 1 = 0 <\/p>\n\n\n\n<p>n = Number of real roots in p(s) <\/p>\n\n\n\n<p>\u2234 n = 1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Consider \ud835\udc5d(\ud835\udc60) = \ud835\udc603 + \ud835\udc4e2\ud835\udc602 + \ud835\udc4e1\ud835\udc60 + \ud835\udc4e0 with all real coefficients. It is known that its derivative \ud835\udc5d\u2032(\ud835\udc60) has no real roots. The number of real roots of \ud835\udc5d(\ud835\udc60) is (A) 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (C) 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (D) 3 Ans: 1 Sol: Given p(s) = s3 + a2\u00a0s2 + a1s + a0 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160478,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-160477","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=160477"}],"version-history":[{"count":2,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160477\/revisions"}],"predecessor-version":[{"id":160480,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160477\/revisions\/160480"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160478"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}