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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
Solving by completing square
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