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Example 9 - Find roots of 4x2 + 3x + 5 = 0 by completing sq - Examples

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Example 9 Find the roots of 4x2 + 3x + 5 = 0 by the method of completing the square. 4x2 + 3x + 5 = 0 Dividing by 4 4๐‘ฅ2/4+3๐‘ฅ/4+5/4=0 x2 + 3๐‘ฅ/4+5/4=0 We know that (a + b)2 = a2 + 2ab + b2 Here, a = x & 2ab = 3๐‘ฅ/4 2xb = 3๐‘ฅ/4 2b = 3/4 b = 3/4ร—1/2 b = 3/8 Now, in our equation x2 + 3๐‘ฅ/4+5/4=0 Adding and subtracting (3/8)^2 x2 + 3๐‘ฅ/4+5/4+(3/8)^2โˆ’(3/8)^2=0 x2 + 3๐‘ฅ/4+(3/8)^2+5/4โˆ’(3/8)^2=0 (๐‘ฅ+3/8)^2+5/4โˆ’(3/8)^2=0 (๐‘ฅ+3/8)^2=(3/8)^2โˆ’5/4 (๐‘ฅ+3/8)^2=9/64โˆ’5/4 (๐‘ฅ+3/8)^2=(9 โˆ’ 5(16))/64 (๐‘ฅ+3/8)^2=(9 โˆ’ 80)/64 (๐‘ฅ+3/8)^2=(โˆ’71)/64 Since square of any number cannot be negative So, answer does not exist

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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