Ex 4.3, 1 - Find roots by completing the square (i) 2x2 - - Solving by completing square

Ex 4.3, 1 (i) - Chapter 4 Class 10 Quadratic Equations - Part 2
Ex 4.3, 1 (i) - 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: (i) 2x2 โ€“ 7x + 3 = 0 2x2 โ€“ 7x +3 = 0 Dividing by 2 (2๐‘ฅ2 โˆ’ 7๐‘ฅ + 3 = 0)/2=0/2 2๐‘ฅ2/2 โ€“ 7๐‘ฅ/2 + 3/2=0 x2 โ€“ 7๐‘ฅ/2+3/2=0 We know that (a โ€“ b)2 = a2 โ€“ 2ab + b2 Here, a = x & โ€“ 2ab = โ€“ 7๐‘ฅ/2 โ€“ 2xb = โˆ’7๐‘ฅ/2 b = โˆ’7๐‘ฅ/(2(โˆ’2๐‘ฅ)) b = 7/4 Now, in our equation x2 โˆ’7๐‘ฅ/2+3/2=0 Adding and subtracting (7/4)^2 x2 โˆ’7๐‘ฅ/2+3/2+(7/4)^2โˆ’(7/4)^2=0 x2 +(7/4)^2โˆ’7๐‘ฅ/2+3/2โˆ’(7/4)^2=0 (๐‘ฅโˆ’ 7/4)^2+3/2 โˆ’(7/4)^2=0 (๐‘ฅโˆ’ 7/4)^2+3/2โˆ’49/16=0 (๐‘ฅโˆ’ 7/4)^2+(3(8) โˆ’ 49)/16=0 (๐‘ฅโˆ’ 7/4)^2+(24 โˆ’ 49)/16=0 (๐‘ฅโˆ’ 7/4)^2โˆ’25/16=0 (๐‘ฅโˆ’7/4)^2=25/16 (๐‘ฅโˆ’7/4)^2=(5/4)^2 Cancelling square both sides ๐‘ฅโˆ’7/4 = ยฑ 5/4

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