2<\/sup> – x – 4 \n\u21d2 3x\u00b2 – 4x + 3x – 4 \n\u21d2 x(3x – 4) + 1(3x – 4) \n\u21d2 (3x – 4) (x + 1) \n3x – 4 = 0 or x + 1 = 0 \n\u21d2 x = \\(\\frac { 4 }{ 3 }\\) or x = – 1 \nVerification: \n <\/p>\n <\/p>\n
Question 2. \nFind a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. \n(i) \\(\\frac { 1 }{ 4 }\\), – 1 \n(ii) \\(\\sqrt{2}\\), \\(\\frac { 1 }{ 3 }\\) \n(iii) 0, \\(\\sqrt{5}\\) \n(iv) 1, 1 \n(v) \\(\\frac { -1 }{ 4 }\\), \\(\\frac { 1 }{ 4 }\\) \n(vi) 4, 1 \nSolution: \n(i) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = \\(\\frac { 1 }{ 4 }\\) = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = – 1 = \\(\\frac { c }{ a }\\) \nIf a = 4, then b = – 1 and c = – 4 \nSo, one quadratic polynomial which fits the given condition is 4x\u00b2 – x – 4.<\/p>\n
(ii) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = \\(\\sqrt{2}\\) = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = \\(\\frac { 1 }{ 3 }\\) = \\(\\frac { c }{ a }\\) \nIf a = 4, then b = – \\(\\sqrt{2}\\) and c = \\(\\frac { 1 }{ 3 }\\) \nSo, one quadratic polynomial which fits the given condition is x\u00b2 – \\(\\sqrt{2x}\\) + \\(\\frac { 1 }{ 3 }\\) or 3x\u00b2 – 3\\(\\sqrt{2x}\\) + 1<\/p>\n
(iii) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = 0 = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = \\(\\sqrt{5}\\) = \\(\\frac { c }{ a }\\) \nIf a = 1, then b = 0 and c = \\(\\sqrt{5}\\) \nSo, one quadratic polynomial which fits the given condition is x\u00b2 – \\(\\sqrt{5}\\)<\/p>\n
(iv) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = 1 = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = 1 = \\(\\frac { c }{ a }\\) \nIf a = 1, then b = – 1 and c = 1 \nNow, put the values of a, b and c in equation ax\u00b2 + bx + c \nSo, one quadratic polynomial which fits the given condition is x\u00b2 – \\(\\sqrt{5}\\) \n1x\u00b2 – 1x 1 = 0 \nor x\u00b2 – x + 1 = 0<\/p>\n
(v) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = –\\(\\frac { 1 }{ 4 }\\) = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = \\(\\frac { 1 }{ 4 }\\) = \\(\\frac { c }{ a }\\) \nIf a = 1, then b = 1 and c = 1 \nNow, put the values of a, b and c in equation ax\u00b2 + bx + c \nSo, one quadratic polynomial which fits the given condition is 4x\u00b2 + x + 1 = 0<\/p>\n
(vi) Let the polynomial be ax\u00b2 + bx + c and its zeroes be \u03b1 and \u00df. \nThen \u03b1 + \u03b2 = 4 = \\(\\frac { -b }{ a }\\) \nand \u03b1.\u03b2 = 1 = \\(\\frac { c }{ a }\\) \nIf a = 1, then b = – 4 and c = 1 \nSo, one quadratic polynomial which fits the given condition is x\u00b2 – 4x + 1 = 0<\/p>\n
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These NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.2 Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) …<\/p>\n
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2<\/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 2 Polynomials Ex 2.2 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n