Example 7 - Solve 2x2 - 5x + 3 = 0 by completing the square - Solving by completing square

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
Ask Download

Transcript

Example 7 Solve the equation given in Example 3 (2x2 โ€“ 5x + 3 = 0) by the method of completing the square. 2x2 โ€“ 5x + 3 = 0 Dividing by 2 (2๐‘ฅ2 โˆ’ 5๐‘ฅ + 3)/2=0/2 2๐‘ฅ2/2โˆ’5๐‘ฅ/2+3/2=0 x2 โ€“ 5๐‘ฅ/2+3/2=0 We know that (a โ€“ b)2 = a2 โ€“ 2ab + b2 Here, a = x & โ€“ 2ab = (โˆ’ 5๐‘ฅ)/2 โ€“ 2xb = (โˆ’ 5๐‘ฅ)/2 โ€“ 2b = (โˆ’ 5)/2 b = (โˆ’ 5)/(2(โˆ’2)) b = 5/4 Now, in our equation x2 โ€“ 5๐‘ฅ/2+3/2=0 Adding and subtracting (5/4)^2 x2 โ€“ 5๐‘ฅ/2+3/2+(5/4)^2โˆ’(5/4)^2=0 x2 +(5/4)^2โ€“ 5๐‘ฅ/2+3/2โˆ’(5/4)^2=0 (๐‘ฅโˆ’5/4)^2 +3/2โˆ’(5/4)^2=0 (๐‘ฅโˆ’5/4)^2 +3/2โˆ’25/16=0 (๐‘ฅโˆ’5/4)^2=25/16 โˆ’ 3/2 (๐‘ฅโˆ’5/4)^2=(25 โˆ’ 3(8))/16 (๐‘ฅโˆ’5/4)^2=(25 โˆ’ 24)/16 (๐‘ฅโˆ’5/4)^2=1/16 (๐‘ฅโˆ’5/4)^2=(1/4)^2 Cancelling square ๐‘ฅโˆ’5/4 = ยฑ 1/4 ๐‘ฅโˆ’5/4 = ยฑ 1/4 Solving So, the roots of the equation are x = 3/2 & x = 1

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
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.
Jail