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
  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.