Learn all Concepts of Chapter 4 Class 10 (with VIDEOS). Check - Quadratic Equations - Class 10


Last updated at Dec. 8, 2020 by Teachoo
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 (2๐ฅ2 โ 7๐ฅ + 3 = 0)/2=0/2 2๐ฅ2/2 โ 7๐ฅ/2 + 3/2=0 x2 โ 7๐ฅ/2+3/2=0 We know that (a โ b)2 = a2 โ 2ab + b2 Here, a = x & โ 2ab = โ 7๐ฅ/2 โ 2xb = โ7๐ฅ/2 b = โ7๐ฅ/(2(โ2๐ฅ)) b = 7/4 Now, in our equation x2 โ7๐ฅ/2+3/2=0 Adding and subtracting (7/4)^2 x2 โ7๐ฅ/2+3/2+(7/4)^2โ(7/4)^2=0 x2 +(7/4)^2โ7๐ฅ/2+3/2โ(7/4)^2=0 (๐ฅโ 7/4)^2+3/2 โ(7/4)^2=0 (๐ฅโ 7/4)^2+3/2โ49/16=0 (๐ฅโ 7/4)^2+(3(8) โ 49)/16=0 (๐ฅโ 7/4)^2+(24 โ 49)/16=0 (๐ฅโ 7/4)^2โ25/16=0 (๐ฅโ7/4)^2=25/16 (๐ฅโ7/4)^2=(5/4)^2 Cancelling square both sides ๐ฅโ7/4 = ยฑ 5/4
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