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: (ii) 2x2 + x โ€“ 4 = 0 2x2 + x โ€“ 4 = 0 Dividing whole equation by 2 (2๐‘ฅ2 + ๐‘ฅ โˆ’ 4)/2=0/2 2๐‘ฅ2/2+๐‘ฅ/2โˆ’4/2=0 x2 + ๐‘ฅ/2โˆ’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 = 1/2 ร— 1/2 b = 1/4 Now, in our equation x2 + ๐‘ฅ/2โˆ’2=0 Adding and subtracting (1/4)^2 x2 + ๐‘ฅ/2โˆ’2+(1/4)^2โˆ’(1/4)^2= 0 x2 + ๐‘ฅ/2+(1/4)^2โ€“ 2 โ€“ (1/4)^2=0 (๐‘ฅ+1/4)^2โˆ’2โˆ’(1/4)^2= 0 (๐‘ฅ+1/4)^2โˆ’2 โˆ’1/16=0 (๐‘ฅ+1/4)^2=2+1/16 (๐‘ฅ+1/4)^2=(2(16) + 1)/16 (๐‘ฅ+1/4)^2=(32 + 1)/16 (๐‘ฅ+1/4)^2=33/16 (๐‘ฅ+1/4)^2=(โˆš33/4)^2 Cancelling square both sides ๐‘ฅ+1/4 = ยฑ โˆš33/4 Solving So, the root of the equation are x = (โˆš33 โˆ’ 1)/4 & x = (โˆ’(โˆš33 + 1))/4

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.