{"id":2329,"date":"2025-01-04T15:30:21","date_gmt":"2025-01-04T10:00:21","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=2329"},"modified":"2025-02-05T10:22:54","modified_gmt":"2025-02-05T04:52:54","slug":"samacheer-kalvi-12th-maths-guide-chapter-3-ex-3-4","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-12th-maths-guide-chapter-3-ex-3-4\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 3 Theory of Equations Ex 3.4"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 3 Theory of Equations Ex 3.4 Textbook Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.4<\/h2>\n

Question 1.
\nSolve:
\n(i) (x – 5) (x – 7) (x + 6)(x + 4) = 504
\nSolution:
\n(x – 5) (x + 4) (x – 7) (x + 6) = 504
\n(x2<\/sup> – x – 20) (x2<\/sup> – x – 42) = 504
\nLet y = (x2<\/sup> – x)
\n(y – 20) (y – 42) = 504
\n\u21d2 y2<\/sup> – 42y – 20y + 840 = 504
\n\u21d2 y2<\/sup> – 62y + 336 = 0
\n\u21d2 (y – 56) (y – 6) = 0
\n\u21d2 (y – 56) = 0 or (y – 6) = 0
\n\u21d2 x2<\/sup> – x – 56 = 0 or x2<\/sup> – x – 6 = 0
\n\u21d2 (x – 8) (x + 7) = 0 or (x – 3) (x + 2) = 0
\n\u21d2 x = 8, -7 or x = 3, -2
\nThe roots are 8, -7, 3, -2<\/p>\n

(ii) (x – 4)(x – 2)(x- 7)(x + 1) = 16
\nSolution:
\n(x – 4) (x – 7) (x – 2) (x + 1) = 16
\n\u21d2 (x – 4) (x – 2) (x – 7) (x + 1) = 16
\n\u21d2 (x2<\/sup> – 6x + 8) (x2<\/sup> – 6x – 7) = 16
\nLet x2<\/sup> – 6x = y
\n(y + 8)(y – 7) = 16
\n\u21d2 y2<\/sup> – 7y + 8y – 56 – 16 = 0
\n\u21d2 y2<\/sup> + y – 72 = 0
\n\u21d2 (y + 9) (y – 8) = 0
\ny + 9 = 0
\nx2<\/sup> – 6x + 9 = 0
\n(x – 3)2<\/sup> = 0
\nx = 3, 3
\nor
\ny – 8 = 0
\nx2<\/sup> – 6x – 8 = 0
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nSolve:
\n(2x – 1)(x + 3)(x – 2)(2x + 3) + 20 = 0
\nSolution:
\n(x + 3)(x – 2) (2x – 1)(2x + 3) + 20 = 0
\n(x\u00b2 + x – 6) (4x\u00b2 + 6x – 2x – 3) + 20 = 0
\n(x\u00b2 + x – 6) (4x\u00b2 + 4x – 3) + 20 = 0
\n(x\u00b2 + x – 6) (x\u00b2 + 4x – \\(\\frac{3}{4}\\)) + 20 = 0
\n(\u00f74) (x\u00b2 + x – 6) (x\u00b2 + x – \\(\\frac{3}{4}\\)) + \\(\\frac{20}{4}\\) = 0
\nPut y = x\u00b2 + x
\n\"Samacheer
\n4y\u00b2 – 27y – 38 = 0
\n4y\u00b2 – 8y – 19y + 38 = 0
\n(4y – 19) (y – 2) = 0
\ny = 2 (or) y = \\(\\frac{19}{4}\\)
\nx\u00b2 + x = 2 (or) x\u00b2 + x = \\(\\frac{19}{4}\\)
\nx\u00b2 + x – 2 = 0 (or) 4x\u00b2 + 4x = 19
\n(x + 2)(x – 1) = 0 (or) 4x\u00b2 + 4x – 19 = 0
\nx = -2 or x = 1
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.4 Textbook Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.4 Question 1. Solve: (i) (x – 5) (x – 7) (x + 6)(x + 4) = 504 Solution: (x – …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[5],"tags":[],"class_list":["post-2329","post","type-post","status-publish","format-standard","hentry","category-class-12"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2329"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=2329"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2329\/revisions"}],"predecessor-version":[{"id":40091,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/2329\/revisions\/40091"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=2329"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=2329"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=2329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}