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Find roots of 2x^2 + x + 4 = 0 by Completing the Square - Teachoo

Ex 4.3, 1 (iv) - Chapter 4 Class 10 Quadratic Equations - Part 2

Ex 4.3, 1 (iv) - Chapter 4 Class 10 Quadratic Equations - Part 3

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Ex 4.3 ,1 Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iv) 2x2 + x + 4 = 0 2x2 + x + 4 = 0 Dividing equation by 2 (2π‘₯2 + π‘₯ + 4)/2=0/2 2π‘₯2/2+π‘₯/2 + 4/2=0 x2 + π‘₯/2+2=0 We know that (a + b)2 = a2 + 2ab + b2 Here, a = x & 2ab = π‘₯/2 2xb = π‘₯/2 2b = 1/2 b = 1/2Γ—1/2 b = 1/4 Now, in our equation x2 + π‘₯/2+2=0 Adding and subtracting (1/4)^2 x2 + π‘₯/2 +2+(1/4)^2βˆ’(1/4)^2=0 "x2 + " π‘₯/2+(1/4)^2+2βˆ’(1/4)^2=0 (π‘₯+1/4)^2+2βˆ’(1/4)^2=0 (π‘₯+1/4)^2+2βˆ’1/16=0 (π‘₯+1/4)^2+((32 βˆ’ 1)/16)=0 (π‘₯+1/4)^2+ 31/16=0 (π‘₯+1/4)^2=(βˆ’31)/16 Since square of any number cannot be negative So, answer does not exist

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.