1. Class 10
2. Important Questions for Exam - Class 10

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Example 8 Find the roots of the equation 5x2 โ 6x โ 2 = 0 by the method of completing the square. 5x2 โ 6x โ 2 = 0 Dividing by 5 (5๐ฅ2 โ 6๐ฅ โ 2)/5=0/5 5๐ฅ2/5โ6๐ฅ/5โ2/5=0 x2 โ 6๐ฅ/5โ2/5=0 We know that (a โ b)2 = a2 โ 2ab + b2 Here, a = x & โ 2ab = (โ 6๐ฅ)/5 โ 2xb = (โ 6๐ฅ)/5 โ 2b = (โ 6)/5 b = (โ6)/(5 ร (โ2)) b = 3/5 Now, in our equation x2 โ 6๐ฅ/5โ2/5=0 Adding and subtracting (3/5)^2 x2 โ 6๐ฅ/5โ2/5+(3/5)^2โ(3/5)^2=0 x2 โ 6๐ฅ/5+(3/5)^2โ2/5โ(3/5)^2=0 (๐ฅโ3/5)^2โ2/5โ(3/5)^2=0 (๐ฅโ3/5)^2=(3/5)^2+2/5 (๐ฅโ3/5)^2=9/25+2/5 (๐ฅโ3/5)^2=(9 + 2(5))/25 (๐ฅโ3/5)^2=(9 +10)/25 (๐ฅโ3/5)^2=19/25 (๐ฅโ3/5)^2=(โ19)^2/5^2 Cancelling squares both sides ๐ฅโ3/5 = ยฑ โ19/5 ๐ฅโ3/5 = ยฑ โ19/5 Solving So, x = (โ(19 )+ 3)/5 and x = (โ โ19 + 3)/5 are the roots of the equation .

Class 10
Important Questions for Exam - Class 10