{"id":6033,"date":"2023-08-06T16:30:23","date_gmt":"2023-08-06T16:30:23","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6033"},"modified":"2023-08-06T16:30:23","modified_gmt":"2023-08-06T16:30:23","slug":"ncert-solutions-class-10-maths-chapter-4-quadratic-equations-ex-4-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-4-quadratic-equations-ex-4-1\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 4 (Quadratic Equations)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 4 Quadratic Equations <\/strong>Exercise 4.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter : 4 Quadratic Equations<\/strong> <\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-4-quadratic-equations-ex-4-2\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 4.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-4-quadratic-equations-ex-4-3\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 4.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-4-quadratic-equations-ex-4-4\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 4.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 4.1<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Check whether the following are quadratic equations:<br \/>\n<\/strong><strong>(i)<\/strong> (x + 1)<sup>2<\/sup>\u00a0= 2(x \u2013 3)<br \/>\n<strong>(ii)<\/strong> x<sup>2<\/sup>\u00a0\u2013 2x = (\u20132) (3 \u2013 x)<br \/>\n<strong>(iii)<\/strong> (x \u2013 2)(x + 1) = (x \u2013 1)(x + 3)<br \/>\n<strong>(iv)<\/strong> (x \u2013 3)(2x +1) = x(x + 5)<br \/>\n<strong>(v)<\/strong> (2x \u2013 1)(x \u2013 3) = (x + 5)(x \u2013 1)<br \/>\n<strong>(vi)<\/strong> x<sup>2<\/sup>\u00a0+ 3x + 1 = (x \u2013 2)<sup>2<br \/>\n<\/sup><strong>(vii)<\/strong> (x + 2)<sup>3<\/sup>\u00a0= 2x (x<sup>2<\/sup>\u00a0\u2013 1)<br \/>\n<strong>(viii)<\/strong> x<sup>3<\/sup>\u00a0\u2013 4x<sup>2<\/sup>\u00a0\u2013 x + 1 = (x \u2013 2)<sup>3<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i)<\/strong> (<i>x<\/i>\u00a0+ 2)<sup>2<\/sup>\u00a0= 2(<i>x<\/i> &#8211; 3)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 2<i>x<\/i>\u00a0+ 1 = 2<i>x<\/i>\u00a0&#8211; 6<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 7 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii)\u00a0<\/strong><i>x<\/i><sup>2<\/sup>\u00a0&#8211; 2<i>x<\/i>\u00a0= (-2)(3 &#8211;\u00a0<i>x<\/i>)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>&#8211;<sup>\u00a0<\/sup>2<i>x = &#8211;<\/i>6\u00a0+ 2<i>x\u00a0<\/i><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>&#8211; 4<i>x<\/i>\u00a0+ 6 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii)<\/strong> (<i>x<\/i>\u00a0&#8211; 2)(<i>x<\/i>\u00a0+ 1) = (<i>x<\/i>\u00a0&#8211; 1)(<i>x<\/i>\u00a0+ 3)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>&#8211;\u00a0<i>x<\/i>\u00a0&#8211; 2 =\u00a0<i>x<\/i><sup>2\u00a0<\/sup>+ 2<i>x<\/i>\u00a0&#8211; 3<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 3<i>x<\/i>\u00a0&#8211; 1 =0<\/span><br \/>\n<span style=\"color: #000000;\">It is not of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>not a quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv)<\/strong> (<i>x<\/i>\u00a0&#8211; 3)(2<i>x<\/i>\u00a0+ 1) =\u00a0<i>x<\/i>(<i>x<\/i>\u00a0+ 5)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 2<i>x<\/i><sup>2\u00a0<\/sup>&#8211; 5<i>x<\/i>\u00a0&#8211; 3 =\u00a0<i>x<\/i><sup>2\u00a0<\/sup>+ 5<i>x<\/i><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 \u00a0<i>x<\/i><sup>2\u00a0<\/sup>&#8211; 10<i>x<\/i>\u00a0&#8211; 3 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v)<\/strong> (2<i>x<\/i>\u00a0&#8211; 1)(<i>x<\/i>\u00a0&#8211; 3) = (<i>x<\/i>\u00a0+ 5)(<i>x<\/i>\u00a0&#8211; 1)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 2<i>x<\/i><sup>2\u00a0<\/sup>&#8211; 7<i>x\u00a0+<\/i>\u00a03 =\u00a0<i>x<\/i><sup>2\u00a0<\/sup>+ 4<i>x\u00a0<\/i>&#8211; 5<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>&#8211; 11<i>x<\/i>\u00a0+\u00a08 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vi)<\/strong> <i>x<\/i><sup>2<\/sup>\u00a0+ 3<i>x<\/i>\u00a0+ 1 = (<i>x<\/i>\u00a0&#8211; 2)<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 3<i>x<\/i>\u00a0+ 1\u00a0=\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 4\u00a0&#8211; 4<i>x<\/i><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 7<i>x<\/i>\u00a0&#8211; 3 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is not of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>not a quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vii)<\/strong> (<i>x<\/i>\u00a0+ 2)<sup>3<\/sup>\u00a0= 2<i>x<\/i>(<i>x<\/i><sup>2<\/sup>\u00a0&#8211; 1)<\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>3<\/sup>\u00a0+ 8\u00a0+\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 12<i>x<\/i>\u00a0= 2<i>x<\/i><sup>3<\/sup>\u00a0&#8211; 2<i>x<\/i><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2\u00a0<i>x<\/i><sup>3<\/sup>\u00a0+ 14<i>x<\/i>\u00a0&#8211; 6<i>x<\/i><sup>2<\/sup>\u00a0&#8211; 8 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is not of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>not a quadratic equation<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(viii)\u00a0<\/strong><i>x<\/i><sup>3<\/sup>\u00a0&#8211; 4<i>x<\/i><sup>2<\/sup>\u00a0&#8211;\u00a0<i>x<\/i>\u00a0+ 1 = (<i>x<\/i>\u00a0&#8211; 2)<sup>3<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 \u00a0<i>x<\/i><sup>3<\/sup>\u00a0&#8211; 4<i>x<\/i><sup>2<\/sup>\u00a0&#8211;\u00a0<i>x<\/i>\u00a0+ 1\u00a0=\u00a0<i>x<\/i><sup>3<\/sup>\u00a0&#8211; 8 &#8211; 6<i>x<\/i><sup>2\u00a0<\/sup>\u00a0+ 12<i>x<\/i><\/span><br \/>\n<span style=\"color: #000000;\">\u21d2 2<i>x<\/i><sup>2<\/sup>\u00a0&#8211; 13<i>x<\/i>\u00a0+ 9 = 0<\/span><br \/>\n<span style=\"color: #000000;\">It is of the form\u00a0<i>ax<\/i><sup>2<\/sup>\u00a0+\u00a0<i>bx<\/i>\u00a0+\u00a0<i>c<\/i>\u00a0= 0.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the given equation is <strong>quadratic equation<\/strong>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Represent the following situations in the form of quadratic equations:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) The area of a rectangular plot is 528 m<sup>2<\/sup>. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211;\u00a0<\/strong>Let the breadth of the rectangular plot =\u00a0<i>x<\/i>\u00a0m<br \/>\nHence, the length of the plot is (2<i>x<\/i>\u00a0+ 1) m.<br \/>\nFormula of area of rectangle = length\u00a0\u00d7\u00a0breadth = 528 m<sup>2<\/sup><br \/>\nPutting the value of length and width, we get<br \/>\n(2<i>x\u00a0<\/i>+ 1) \u00d7\u00a0<i>x<\/i>\u00a0= 528<br \/>\n\u21d2 2<i>x<\/i><sup>2<\/sup>\u00a0+\u00a0<i>x<\/i>\u00a0=528<br \/>\n\u21d2 2<i>x<\/i><sup>2<\/sup>\u00a0+\u00a0<i>x<\/i>\u00a0&#8211; 528 = 0<br \/>\nThus, the\u00a0quadratic equation\u00a0is 2x<sup>2<\/sup>\u00a0+ x &#8211; 528 = 0 , where x is the breadth of the rectangular plot.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) The product of two consecutive positive integers is 306. We need to find the integers.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211;\u00a0<\/strong>Let the first integer number =\u00a0<i>x<\/i><br \/>\nNext consecutive positive integer will =\u00a0<i>x<\/i>\u00a0+ 1<br \/>\nProduct of both integers =\u00a0<i>x<\/i>\u00a0\u00d7\u00a0(<i>x<\/i>\u00a0+1) = 306<br \/>\n\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>+\u00a0<i>x<\/i>\u00a0= 306<br \/>\n\u21d2\u00a0<i>x<\/i><sup>2\u00a0<\/sup>+\u00a0<i>x<\/i>\u00a0&#8211; 306 = 0<br \/>\nThus, the quadratic equation is\u00a0x<sup>2<\/sup>\u00a0+ x &#8211; 306 = 0 where x is the first integer.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) Rohan\u2019s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan\u2019s present age.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211;\u00a0<\/strong>Let take Rohan&#8217;s age =\u00a0<i>x<\/i>\u00a0years<br \/>\nHence, his mother&#8217;s age =\u00a0<i>x<\/i>\u00a0+ 26<br \/>\n3 years from now<br \/>\nRohan&#8217;s age =\u00a0<i>x<\/i>\u00a0+ 3<br \/>\nAge of Rohan&#8217;s mother will =\u00a0<i>x<\/i>\u00a0+ 26 + 3 =\u00a0<i>x<\/i>\u00a0+ 29<br \/>\nThe product of their ages 3 years from now will be 360 so that<br \/>\n(<i>x<\/i>\u00a0+ 3)(<i>x<\/i>\u00a0+ 29) = 360<br \/>\n\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 29<i>x<\/i>\u00a0+ 3<i>x<\/i>\u00a0+ 87 = 360<br \/>\n\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 32<i>x<\/i>\u00a0+ 87 &#8211; 360 = 0<br \/>\n\u21d2\u00a0<i>x<\/i><sup>2<\/sup>\u00a0+ 32<i>x<\/i>\u00a0&#8211; 273 = 0<br \/>\nThus, the quadratic equation is x<sup>2<\/sup>\u00a0+ 32x &#8211; 273 = 0 where x is the present age of Rohan.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km\/h less, then it would have taken<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211;\u00a0<\/strong>Let the speed of train be\u00a0<i>x<\/i>\u00a0km\/h.<\/span><br \/>\n<span style=\"color: #000000;\">Time taken to travel 480 km = 480\/<i>x<\/i>\u00a0km\/h<\/span><br \/>\n<span style=\"color: #000000;\">In second condition, let the speed of train = (<i>x<\/i>\u00a0&#8211; 8) km\/h<br \/>\nIt is also given that the train will take 3 hours to cover the same distance.<br \/>\nTherefore, time taken to travel 480 km = (480\/<i>x<\/i>\u00a0+ 3) km\/h<br \/>\nSpeed \u00d7 Time = Distance<\/span><br \/>\n<span style=\"color: #000000;\">(<em>x<\/em>\u00a0\u2013 8)(480\/<em>x<\/em>\u00a0)+ 3 = 480<br \/>\n\u21d2 480\u00a0+ 3<em>x<\/em>\u00a0\u2013 3840\/<em>x<\/em>\u00a0\u2013 24 = 480<br \/>\n\u21d2 3<em>x<\/em>\u00a0\u2013 3840\/<em>x<\/em>\u00a0= 24<br \/>\n\u21d2\u00a0<em>x<\/em><sup>2\u00a0<\/sup>\u2013 8<em>x<\/em>\u00a0\u2013 1280 = 0<br \/>\nThus, the quadratic equation is x<sup>2<\/sup> &#8211; 8x &#8211; 1280 = 0, where s is the speed of the train.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\"><span style=\"color: #0000ff;\"><b><i>Go Back To Chapters<\/i><\/b><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 4 (Quadratic Equations)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 4 Quadratic Equations Exercise 4.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 4 Quadratic Equations NCERT Class 10 Maths Solution Ex &#8211; 4.2 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1069,1070,1044,1049,1048],"class_list":["post-6033","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-4-quadratic-equations-solutions","tag-ncert-class-10-mathematics-exercise-4-1-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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