{"id":26061,"date":"2022-06-05T12:00:06","date_gmt":"2022-06-05T06:30:06","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=26061"},"modified":"2022-05-23T15:49:55","modified_gmt":"2022-05-23T10:19:55","slug":"ncert-solutions-for-class-10-maths-chapter-4-ex-4-4","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-4-ex-4-4\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4"},"content":{"rendered":"

These NCERT Solutions for Class 10 Maths<\/a> Chapter Ex 4.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.4<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nFind the nature of the roots of the following quadratic equations. If the real roots exist, find them:
\n(i) 2x\u00b2 – 3x + 5 = 0
\n(ii) 3x2<\/sup> – 4\u221a3x + 4 = 0
\n(iii) 2x2<\/sup>-6x + 3 = 0
\nSolution:
\n(i) We have,
\n2x\u00b2 – 3x + 5 = 0
\nHere, a = 2, b = – 3 and c = 5
\n\u2234 Discriminant (D) = b\u00b2 – 4ac = (- 3)\u00b2 – 4 x 2 x 5 = 9 – 40 = – 31
\n\u2234 D= – 31
\nHere, discriminant (D) < 0 Therefore, the given quadratic equation has no real roots.<\/p>\n

(ii) We have, 3x\u00b2 – 4\\(\\sqrt{3x}\\) + 4 = 0
\nHere, a = 3, b= – 4\\(\\sqrt{3x}\\) and c = 4
\n\u2234 Discriminant (D) = b\u00b2 – 4ac = \\((-4 \\sqrt{3 x})^{2}\\) x 4 = 48 – 48
\n\u2234 Discriminant (D) = 0
\nTherefore, the given quadratic equation has two equal real roots.
\n\"NCERT<\/p>\n

(iii) We have, 2x\u00b2 – 6x + 3 = 0
\nHere, a = 2,b = – 6, c = 3
\n\u2234 Discriminant (D) = b\u00b2 – 4ac = (- 6)2 – 4 x 2 x 3 = 36 – 24 = 12
\n\u2234 D= 12 Discriminant (D) > 0
\nTherefore, the given quadratic equation has two distinct real roots. Distinct roots \\(\\sqrt{3x}\\)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nFind the value of k for each of the following quadratic equations, so that they have two real equal roots.
\n(i) 2x\u00b2 + kx + 3 = 0
\n(ii) kx(x – 2) + 6 = 0
\nSolution:
\n(i) We have,
\n2x\u00b2 + kx + 3 = 0
\nHere, a = 2, b = k and c = 3
\n\u2234 Discriminant (D) = b\u00b2 – 4ac = k\u00b2 – 4 x 2 x 3
\nD = k\u00b2 – 24
\nBut we have given that equation has two real and equal roots.
\n\u2234 D = 0
\nk\u00b2 – 24 = 0
\nk\u00b2 = 24
\n\u2234 k = \\(\\sqrt{24}\\)
\nk = \u00b12\\(\\sqrt{6}\\)<\/p>\n

(ii) We have,
\nkx (x – 2) + 6 = 0
\nor, kx\u00b2 – 2kx + 6 = 0
\nHere, a = k, b = – 2k and c = 6
\n\u2234 Discriminant (D) = b\u00b2- 4ac
\n= (- 2k)\u00b2 – 4 x k x 6
\nD= 4k\u00b2 – 24k
\nBut we have given that equation has two real equal roots.
\n\u2234 D = 0
\n4k\u00b2 – 24k = 0
\nor, 4k(k – 6) = 0
\nSo, 4k = 0 or k – 6 = 0
\nTherefore, k = 0 or k = 6<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nIs it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800m2 ? If so, find its length and breadth.
\nSolution:
\nLet breadth of rectangular mango grove = x
\n\u2234 length of rectangular mago grove = 2x
\n\u2234 Area of rectangular mango grove = l x b
\nor 800 = x \u00d7 2x [\u2234 Area of rectangle = Length x Breadth]
\nor 800 = 2x\u00b2
\nor x = \\(\\frac { 800 }{ 2 }\\)
\n\u2234 x = \\(\\sqrt{400}\\) = \u00b1 20
\nSince, dimensions cannot be in negative, so we reject the value of x = – 20.
\n\u2234 Breadth of rectangular mango grove = x = 20 m
\nand length of rectangular mango grove = 2x – 2 x 20 = 40m<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nIs the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
\nSolution:
\nLet the present age of one friend be x
\n\u2234 the present age of other friend be 20 – x
\nFour years ago age of first friend = x – 4
\nand four years ago age of second friend = (20 – x) – 4 = 16 – x
\n\u2234 According to question,
\n(x – 4) (16 – x) = 48
\nor 16x – x\u00b2 – 64 + 4x = 48
\nor – x\u00b2 + 20x – 64 = 48
\nor x\u00b2 – 20x + 64 + 48 = 0
\nor x\u00b2 – 20x + 112 = 0
\nHere, a 1,b = -20 and c = 112
\n\u2234 Discriminant (D) b\u00b2 – 4ac
\n= (-20)2 – 4 x 1 x 112
\n= 440 – 448 = -48
\n\u2234 D<0
\nSo, the equation has no any real roots.
\nTherefore, the given situation is not possible.<\/p>\n

\"NCERT<\/p>\n

Question 5.
\nIt is possible to design a rectangulat park of perimeter 80 m and area 400 m\u00b2? If so find its length and breadth.
\nSolution:
\nLet the length of the rectangular park = x
\n\u2234 the breadth of the rectangular park = (40 – x)
\n\u2234 Area of rectangular park = Length x Breadth
\nor 400 = x(40 – x)
\nor 400 = 40x – x\u00b2
\nor x\u00b2 – 40x + 400 = 0
\nHere, a = 1, b = -40 and c = 400
\n\u2234 Discriminant (D) = b\u00b2 – 4ac
\n= (- 40)\u00b2 – 4 x 1 x 400
\n= 1600 – 1600
\nD = 0
\nTherefore, equation has two real and equal roots.
\n\\(\\begin{aligned}
\nx &=\\frac{-b \\pm \\sqrt{b^{2}-4 a c}}{2 a} \\\\
\n&=\\frac{-(-40) \\pm \\sqrt{0}}{2 \\times 1}=\\frac{40}{2}=20
\n\\end{aligned}\\)
\nSo, the length of rectangular park = x = 20 m
\nand the breadth of rectangular park = (40 -x)
\n= 40 – 20 = 20 m.<\/p>\n

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

These NCERT Solutions for Class 10 Maths Chapter Ex 4.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.4 Question 1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x\u00b2 …<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[2],"tags":[],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-4-ex-4-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 10 Maths Chapter Ex 4.4 Questions and Answers are prepared by our highly skilled subject experts. 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