{"id":34611,"date":"2018-12-26T09:10:26","date_gmt":"2018-12-26T09:10:26","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=34611"},"modified":"2020-11-27T13:59:53","modified_gmt":"2020-11-27T08:29:53","slug":"ncert-solutions-for-class-10-maths-chapter-4-ex-4-3","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-4-ex-4-3\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3"},"content":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 are part of <a class=\"button-red\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths\/\">NCERT Solutions for Class 10 Maths<\/a>. Here are we have given Chapter 4 <strong>Quadratic Equations\u00a0Class 10 NCERT Solutions Ex 4.3.\u00a0<\/strong><\/p>\n<ul>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-4\/\" target=\"_blank\" rel=\"noopener\">Quadratic Equations Class 10 Ex 4.1<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.2\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-4-ex-4-2\/\" target=\"_blank\" rel=\"noopener\">Quadratic Equations Class 10 Ex 4.2<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-4-ex-4-4\/\" target=\"_blank\" rel=\"noopener\">Quadratic Equations Class 10 Ex 4.4<\/a><\/li>\n<\/ul>\n<table style=\"table-layout: fixed; width: 650px;\" border=\"1\">\n<tbody>\n<tr>\n<td><strong>Board<\/strong><\/td>\n<td>CBSE<\/td>\n<\/tr>\n<tr>\n<td><strong>Textbook<\/strong><\/td>\n<td>NCERT<\/td>\n<\/tr>\n<tr>\n<td><strong>Class<\/strong><\/td>\n<td>Class 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Subject<\/strong><\/td>\n<td>Maths<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter<\/strong><\/td>\n<td>Chapter 4<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter Name<\/strong><\/td>\n<td>Quadratic Equations<\/td>\n<\/tr>\n<tr>\n<td><strong>Exercise<\/strong><\/td>\n<td>Ex 4.3<\/td>\n<\/tr>\n<tr>\n<td><strong>Number of Questions Solved<\/strong><\/td>\n<td>11<\/td>\n<\/tr>\n<tr>\n<td><strong>Category<\/strong><\/td>\n<td>NCERT Solutions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations\u00a0Ex 4.3<\/h2>\n<p style=\"text-align: justify;\">Page No: 87<\/p>\n<p><strong>Question 1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:<br \/>\n<\/strong>(i) 2<em>x<\/em><sup>2<\/sup> \u2013 7<em>x<\/em> +3 = 0<br \/>\n(ii) 2<em>x<\/em><sup>2<\/sup> + <em>x<\/em> \u2013 4 = 0<br \/>\n(iii) 4<em>x<\/em><sup>2<\/sup> + 4\u221a3<em>x<\/em> + 3 = 0<br \/>\n(iv) 2<em>x<\/em><sup>2<\/sup> + <em>x<\/em> + 4 = 0<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100240\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-13.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 13\" width=\"419\" height=\"507\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-13.png 419w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-13-248x300.png 248w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100242\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-14.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 14\" width=\"419\" height=\"381\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-14.png 419w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-14-300x273.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100243\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-15.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 15\" width=\"412\" height=\"161\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-15.png 412w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-15-300x117.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100244\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-16.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 16\" width=\"440\" height=\"321\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-16.png 440w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-16-300x219.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\nHowever, the square of a number cannotbe negative.<br \/>\nTherefore, there is no real root for the given equation.<\/p>\n<p>Concept Insight: Before completing the square of any quadratric equation make sure to make the coefficient of square term <em>x<\/em><sup>2<\/sup> or <em>y<\/em><sup>2<\/sup> unity by dividing the whole equation appropriate real number. Once this is done add and subtract the square of half the coefficient of x or y.<\/p>\n<p><strong>Question 2.<\/strong> Find the roots of the quadratic equations by applying the quadratic formula.<br \/>\n(i) 2<em>x<\/em><sup>2<\/sup> \u2013 7<em>x<\/em> +3 = 0<br \/>\n(ii) 2<em>x<\/em><sup>2<\/sup> + <em>x<\/em> \u2013 4 = 0<br \/>\n(iii) 4<em>x<\/em><sup>2<\/sup> + 4\u221a3<em>x<\/em> + 3 = 0<br \/>\n(iv) 2<em>x<\/em><sup>2<\/sup> + <em>x<\/em> + 4 = 0<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100245\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-17.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 17\" width=\"432\" height=\"339\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-17.png 432w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-17-300x235.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100246\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-18.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 18\" width=\"433\" height=\"486\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-18.png 433w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-18-267x300.png 267w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100247\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-19.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 19\" width=\"429\" height=\"202\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-19.png 429w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-19-300x141.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nHowever, the square of a number cannotbe negative.<br \/>\nTherefore, there is no realroot lbr thegivenequation.<\/p>\n<p>Concept Insights: While applying the quadratic formula be careful in applying the rules of radicals for example<br \/>\n\\(\\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \\neq \\quad a+b \\)<br \/>\n\\(\\sqrt { -k } \\quad \\neq \\quad -\\sqrt { \\sqrt { k } } \\)<\/p>\n<p>Page No: 88<\/p>\n<p><strong>Question 3. Find the roots of the following equations:<\/strong><br \/>\n(i) <em>x<\/em>-1\/<em>x<\/em> = 3, <em>x<\/em> \u2260 0<br \/>\n(ii) 1\/<em>x<\/em>+4 \u2013 1\/<em>x<\/em>-7 = 11\/30, <em>x<\/em> = -4, 7<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100248\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-20.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 20\" width=\"422\" height=\"518\" \/><\/p>\n<p>Concept Insights: Apply the arithmetical simplifications appropriately to reduce the equation to quadratic form.<\/p>\n<p><strong>Question 4.<\/strong> The sum of the reciprocals of Rehman\u2019s ages, (in years) 3 years ago and 5 years from now is 1\/3. Find his present age.<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100249\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-21.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 21\" width=\"506\" height=\"397\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Question 5.<\/strong> In a class test, the sum of Shefali\u2019s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100250\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-22.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 22\" width=\"471\" height=\"251\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Question 6.<\/strong> The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.<\/p>\n<p style=\"text-align: justify;\"><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100251\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-23.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 23\" width=\"520\" height=\"327\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Question 7.<\/strong> The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.<\/p>\n<p style=\"text-align: justify;\"><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100252\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-24.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 24\" width=\"500\" height=\"336\" \/><br \/>\n<strong>Question 8.<\/strong> A train travels 360 km at a uniform speed. If the speed had been 5 km\/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.<\/p>\n<p><strong>Solution :<\/strong><\/p>\n<div class=\"solnBox\">\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100253\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-25.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 25\" width=\"258\" height=\"315\" \/><\/p>\n<p>Concept Insight:\u00a0Use the relation s =d\/t to crack this question and remember here distance is constant so speed and time will vary inversely.<\/p>\n<\/div>\n<\/div>\n<p style=\"text-align: justify;\"><strong>Question 9.<\/strong> Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100255\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-26.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 26\" width=\"468\" height=\"151\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100256\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-27.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 27\" width=\"515\" height=\"411\" \/><\/p>\n<p><strong>Question 10.<\/strong> An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speeds of the express train is 11 km\/h more than that of the passenger train, find the average speed of the two trains.<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100257\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-28.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 28\" width=\"521\" height=\"348\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Question 11.<\/strong> Sum of the areas of two squares is 468 m<sup>2<\/sup>. If the difference of their perimeters is 24 m, find the sides of the two squares.<\/p>\n<p><strong>Solution :<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100258\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-29.gif\" alt=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 29\" width=\"538\" height=\"321\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>We hope the NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 4 Quadratic Equations\u00a0Class 10 NCERT Solutions Ex 4.3.\u00a0 Quadratic Equations Class 10 Ex 4.1 Quadratic Equations Class 10 Ex 4.2 Quadratic Equations Class 10 Ex 4.4 Board CBSE [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[6805],"tags":[36685],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 - A Pluse Topper.com<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 helpful to finish your Home Work. 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