{"id":4574,"date":"2021-03-01T12:18:29","date_gmt":"2021-03-01T06:48:29","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=4574"},"modified":"2021-09-15T11:40:37","modified_gmt":"2021-09-15T06:10:37","slug":"ap-ssc-10th-class-maths-solutions-chapter-5-ex-5-4","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-ssc-10th-class-maths-solutions-chapter-5-ex-5-4\/","title":{"rendered":"AP SSC 10th Class Maths Solutions Chapter 5 Quadratic Equations Ex 5.4"},"content":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions<\/a> Chapter 5 Quadratic Equations Ex 5.4 Textbook Questions and Answers.<\/p>\n

AP State Syllabus SSC 10th Class Maths Solutions 5th Lesson Quadratic Equations Exercise 5.4<\/h2>\n

10th Class Maths 5th Lesson Quadratic Equations Ex 5.4 Textbook Questions and Answers<\/h3>\n

Question 1.
\nFind the nature of the roots of the following quadratic equations. If real roots exist, find them.
\ni) 2x2<\/sup> – 3x + 5 = 0
\nAnswer:
\nGiven: 2x2<\/sup> – 3x + 5 = 0
\na = 2; b = -3; c = 5
\nDiscriminant = b2<\/sup> – 4ac
\nb2<\/sup> – 4ac = (-3)2<\/sup> – 4(2)(5)
\n= 9 – 40
\n= -31 < 0
\n\u2234 Roots are imaginary.<\/p>\n

ii) 3x2<\/sup> – 4\u221a3x + 4 = 0
\nAnswer:
\nGiven: 3x2<\/sup> – 4\u221a3x + 4 = 0
\na = 3; b = -4\u221a3; c = 4
\nb2<\/sup> – 4ac = (-4\u221a3)2<\/sup> – 4(3)(4)
\n= 48 – 48 = 0
\n\u2234 Roots are real and equal and they
\n\\(\\frac{-b}{2a}\\), \\(\\frac{-b}{2a}\\)
\n\"AP<\/p>\n

\"AP<\/p>\n

iii) 2x2<\/sup> – 6x + 3 = 0
\nAnswer:
\nGiven: 2x2<\/sup> – 6x + 3 = 0
\na = 2; b = -6; c = 3
\nb2<\/sup> – 4ac = (-6)2<\/sup> – 4(2)(3)
\n= 36 – 24
\n= 12 > 0
\n\u2234 The roots are real and distinct. They are
\n\"AP<\/p>\n

Question 2.
\nFind the values of k for each of the fol-lowing quadratic equations so that they have two equal roots.
\ni) 2x2<\/sup> + kx + 3 = 0
\nAnswer:
\nGiven : 2x2<\/sup> + kx + 3 = 0 has equal roots
\n\u2234 b2<\/sup> – 4ac = 0
\nHere a = 2; b = k; c = 3
\nb2<\/sup> – 4ac = (k)2<\/sup> – 4(2)(3) = 0
\n\u21d2 k2<\/sup> – 24 = 0
\n\u21d2 k2<\/sup> = 24
\n\u21d2 k = \u221a24 = \u00b1 2\u221a6<\/p>\n

ii) kx(x – 2) + 6 = 0
\nAnswer:
\nGiven: kx(x – 2) + 6 = 0
\nkx2<\/sup> – 2kx + 6 = 0
\nAs this Q.E. has equal roots,
\nb2<\/sup> – 4ac = 0
\nHere
\na = k; b = -2k; c = 6
\n\u2234 b2<\/sup> – 4ac = (-2k)2<\/sup> – 4(k)(6) = 0
\n\u21d2 4k2<\/sup> – 24k = 0
\n\u21d2 4k(k – 6) = 0
\n\u21d2 4k = 0 (or) k – 6 = 0
\n\u21d2 k = 0 (or) 6
\nBut k = 0 is trivial
\n\u2234 k = 6.<\/p>\n

\"AP<\/p>\n

Question 3.
\nIs it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2<\/sup>? If so, find its length and breadth.
\nAnswer:
\nLet the breadth = x m
\nThen length = 2x m
\nArea = length x breadth = x.(2x)
\n= 2x2<\/sup> m2<\/sup>
\nBy problem 2x2<\/sup> = 800 \u21d2 x2<\/sup> = 400
\nand x = \u221a400 = \u00b1 20
\n\u2234 Breadth x = 20 m and
\nlength 2x = 2 \u00d7 20 = 40 m.<\/p>\n

Question 4.
\nThe sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Is the above situation possible? If so, deter\u00acmine their present ages.
\nAnswer:
\nLet the age one of the two friends be x years.
\nThen the age of the other = 20 – x
\nThen, 4 years ago their ages would be (x – 4) and (20 – x – 4) = 16 – x
\n\u2234 Product of their ages 4 years ago = (x – 4) (16 – x)
\nBy problem (x – 4) (16 – x) = 48
\n\u21d2 x(16 – x) – 4(16 – x) = 48
\n\u21d2 16x – x2<\/sup> – 64 + 4x = 48
\n\u21d2 x2<\/sup> – 20x + 112 = 0
\nHere a = 1; b = -20; c = 112
\nb2<\/sup> – 4ac = (-20)2<\/sup> – 4(1) (112)
\n= 400 – 448
\n= -48 < 0
\nThus the roots are not real.
\n\u2234 The situation is not possible.<\/p>\n

\"AP<\/p>\n

Question 5.
\nIs it possible to design a rectangular park of perimeter 80 m and area 400 m2<\/sup>? If so, find its length and breadth.
\nAnswer:
\nGiven: Perimeter of a rectangle 2(1 + b) = 80
\n\u21d2 6 + b = \\(\\frac{80}{2}\\) = 40
\nArea of the rectangle, l \u00d7 b = 400
\nIf possible, let us suppose that length of the rectangle = x m say
\nThen its breadth by equation (1) = 40 – x
\nBy problem area = x . (40 – x) = 400
\n\u21d2 40x – x2<\/sup> = 400
\n\u21d2 x2<\/sup> – 40x + 400 = 0
\nHere a = 1; b = -40; c = +400
\nb2<\/sup> – 4ac = (-40)2<\/sup> – 4(1)(+400)
\n= 1600 – 1600 = 0
\n\u2234 The roots are real and equal.
\nThey are \\(\\frac{-b}{2a}\\), \\(\\frac{-b}{2a}\\)
\ni.e., \\(\\frac{-(-40)}{2 \\times 1}\\) = \\(\\frac{40}{2}\\) = 20
\n\u2234 The dimensions are 20 m, 20 m.
\n(\u2234 The park is in square shape)<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions Chapter 5 Quadratic Equations Ex 5.4 Textbook Questions and Answers. AP State Syllabus SSC 10th Class Maths Solutions 5th Lesson Quadratic Equations Exercise 5.4 10th Class Maths 5th Lesson Quadratic Equations Ex 5.4 Textbook Questions and Answers Question 1. Find the nature of the roots …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/4574"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=4574"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/4574\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=4574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=4574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=4574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}