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

  1. Chapter 4 Class 10 Quadratic Equations (Term 2)
  2. Serial order wise

Transcript

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 (2๐‘ฅ2 + ๐‘ฅ + 4)/2=0/2 2๐‘ฅ2/2+๐‘ฅ/2 + 4/2=0 x2 + ๐‘ฅ/2+2=0 We know that (a + b)2 = a2 + 2ab + b2 Here, a = x & 2ab = ๐‘ฅ/2 2xb = ๐‘ฅ/2 2b = 1/2 b = 1/2ร—1/2 b = 1/4 Now, in our equation x2 + ๐‘ฅ/2+2=0 Adding and subtracting (1/4)^2 x2 + ๐‘ฅ/2 +2+(1/4)^2โˆ’(1/4)^2=0 "x2 + " ๐‘ฅ/2+(1/4)^2+2โˆ’(1/4)^2=0 (๐‘ฅ+1/4)^2+2โˆ’(1/4)^2=0 (๐‘ฅ+1/4)^2+2โˆ’1/16=0 (๐‘ฅ+1/4)^2+((32 โˆ’ 1)/16)=0 (๐‘ฅ+1/4)^2+ 31/16=0 (๐‘ฅ+1/4)^2=(โˆ’31)/16 Since square of any number cannot be negative So, answer does not exist

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.