{"id":22060,"date":"2024-01-10T15:54:20","date_gmt":"2024-01-10T10:24:20","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=22060"},"modified":"2024-01-11T12:26:07","modified_gmt":"2024-01-11T06:56:07","slug":"inter-2nd-year-maths-2a-quadratic-expressions-solutions-ex-3c","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/inter-2nd-year-maths-2a-quadratic-expressions-solutions-ex-3c\/","title":{"rendered":"Inter 2nd Year Maths 2A Quadratic Expressions Solutions Ex 3(c)"},"content":{"rendered":"

Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions<\/a> Inter 2nd Year Maths 2A Quadratic Expressions Solutions Exercise 3(c) will help students to clear their doubts quickly.<\/p>\n

Intermediate 2nd Year Maths 2A Quadratic Expressions Solutions Exercise 3(c)<\/h2>\n

I.<\/span><\/p>\n

Question 1.
\nSolve the following inequations by the algebraic method.
\n(i) 15x2<\/sup> + 4x – 4 \u2264 0
\nSolution:
\n15x2<\/sup> + 4x – 4 \u2264 0
\n\u21d2 15x2<\/sup> – 6x + 10x – 4 \u2264 0
\n\u21d2 3x(5x – 2) + 2(5x – 2) \u2264 0
\n\u21d2 (3x + 2) (5x – 2) \u2264 0
\nCo-efficient of x2<\/sup> = 15 > 0,
\nGiven Expression is \u2264 0
\n\u21d2 x lies between \\(\\frac{-2}{3}\\) and \\(\\frac{2}{5}\\)
\ni.e., \\(\\frac{-2}{3} \\leq x \\leq \\frac{2}{5}\\)<\/p>\n

(ii) x2<\/sup> – 2x + 1 < 0
\nSolution:
\nx2<\/sup> – 2x + 1 < 0
\n\u21d2 (x – 1)2<\/sup> < 0
\nThere is no real value of ‘x’ satisfying this inequality
\nSolution set = \u03a6 (or) Solution does not exist.<\/p>\n

\"Inter<\/p>\n

(iii) 2 – 3x – 2x2<\/sup> \u2265 0
\nSolution:
\n-(2x2<\/sup> + 3x – 2) \u2265 0
\n\u21d2 -(2x2<\/sup> + 4x – x – 2) \u2265 0
\n\u21d2 -[2x(x + 2) – 1(x + 2)] \u2265 0
\n\u21d2 -(2x – 1) (x + 2) \u2265 0
\nCo-efficient of x2<\/sup> = -2 < 0,
\nThe given expression is \u2265 0
\n\u21d2 x lies between -2 and \\(\\frac{1}{2}\\)
\ni.e., -2 \u2264 x \u2264 \\(\\frac{1}{2}\\)<\/p>\n

(iv) x2<\/sup> – 4x – 21 \u2265 0
\nSolution:
\nx2<\/sup> – 4x – 21 \u2265 0
\n\u21d2 x2<\/sup> – 7x + 3x – 21 \u2265 0
\n\u21d2 x(x – 7) + 3(x – 7) \u2265 0
\n\u21d2 (x + 3) (x – 7) \u2265 0
\nCo-efficient of x2<\/sup> = 1 > 0,
\nThe given expression is \u2265 0
\nx does not lie between -3 and 7
\ni.e., {x\/x \u2208 (-\u221e, -3] \u222a [7, \u221e)}<\/p>\n

II.<\/span><\/p>\n

Question 1.
\nSolve the following inequations by graphical method.
\n(i) x2<\/sup> – 7x + 6 > 0
\nSolution:
\nf(x) = x2<\/sup> – 7x + 6
\n\"Inter
\nf(x) > 0 \u21d2 y > 0
\nSolutions are given by x < 1 and x > 6<\/p>\n

(ii) 4 – x2<\/sup> > 0
\nSolution:
\nLet f(x) = 4 – x2<\/sup>
\n\"Inter
\nf(x) > 0 \u21d2 y > 0
\nSolution set = {x\/-2 < x < 2}<\/p>\n

(iii) 15x2<\/sup> + 4x – 4 < 0
\nSolution:
\nLet f(x) = 15x2<\/sup> + 4x – 4
\n\"Inter
\nf(x) \u2264 0 \u21d2 y \u2264 0
\nSolution set = \\(\\left\\{x \/ \\frac{-2}{3} \\leq x \\leq \\frac{2}{5}\\right\\}\\)<\/p>\n

(iv) x2<\/sup> – 4x – 21 \u2265 0
\nSolution:
\nLet f(x) = x2<\/sup> – 4x – 21
\n\"Inter
\nf(x) \u2265 0 \u21d2 y \u2265 0
\nSolution set = {x\/x \u2208 (-\u221e, -3] \u222a [7, \u221e)}<\/p>\n

\"Inter<\/p>\n

Question 2.
\nSolve the following inequations.
\n(i) \\(\\sqrt{3 x-8}\\) < -2
\nSolution:
\nL.H.S. is positive and R.H.S. is negative.
\n\u2234 The given inequality holds for no real x.
\nSolution set = \u03a6 (or) Solution does not exist.<\/p>\n

(ii) \\(\\sqrt{-x^{2}+6 x-5}\\) > 8 – 2x
\nSolution:
\n\\(\\sqrt{-x^{2}+6 x-5}\\) > 8 – 2x
\n\u21d4 -x2<\/sup> + 6x – 5 > 0
\nand (i) 8 – 2x < 0 (or) (ii) 8 – 2x \u2265 0
\nWe have -x2<\/sup> + 6x – 5 = -(x2<\/sup> – 6x + 5) = -(x – 1) (x – 5)
\nHence -x2<\/sup> + 6x – 5 \u2265 0 \u21d4 x \u2208 [1, 5]
\n(i) -x2<\/sup> + 6x – 5 \u2265 0 and 8 – 2x < 0
\n\u21d4 x \u2208 [1, 5] and x > 4
\n\u21d4 x \u2208 [4, 5] ………(1)
\n(ii) -x2<\/sup> + 6x – 5 \u2265 0 and 8 – 2x \u2265 0
\n\u2235 \\(\\sqrt{\\left(-x^{2}+6 x-5\\right)}\\) > 8 – 2x
\n\u21d4 -x2<\/sup> + 6x – 5 > (8 – 2x)2<\/sup> and 8 – 2x \u2265 0
\n\u21d4 -x2<\/sup> + 6x – 5 > 64 + 4x2<\/sup> – 32x and x \u2264 4
\n\u21d4 -5x2<\/sup> + 38x – 69 > 0 and x \u2264 4
\n\u21d4 5x2<\/sup> – 38x + 69 < 0 and x \u2264 4
\n\u21d4 5x2<\/sup> – 15x – 23x + 69 < 0 and x \u2264 4
\n\u21d4 (5x – 23)(x – 3) < 0 and x \u2264 4
\n\u21d4 x \u2208 (3, \\(\\frac{23}{5}\\)) and x \u2264 4
\n\u21d4 x \u2208 (3, \\(\\frac{23}{5}\\)) \u2229 (-\u221e, 4)
\n\u21d4 x \u2208 (3, 4)
\nHence the solution set of the given equation is x \u2208 (4, 5) \u222a (3, 4)
\n\u21d2 x \u2208 (3, 5) (or) 3 < x \u2264 5.<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions Inter 2nd Year Maths 2A Quadratic Expressions Solutions Exercise 3(c) will help students to clear their doubts quickly. Intermediate 2nd Year Maths 2A Quadratic Expressions Solutions Exercise 3(c) I. Question 1. Solve the following inequations by the algebraic method. (i) 15×2 + 4x – 4 \u2264 … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/22060"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=22060"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/22060\/revisions"}],"predecessor-version":[{"id":22061,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/22060\/revisions\/22061"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=22060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=22060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=22060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}