Question 1 (i) - Solving by completing square - Chapter 4 Class 10 Quadratic Equations

Last updated at August 10, 2026 by

Ex 4.3, 1 - Find roots by completing the square (i) 2x2 - - Solving by completing square

Ex 4.3, 1 (i) - Chapter 4 Class 10 Quadratic Equations - Part 2
Ex 4.3, 1 (i) - Chapter 4 Class 10 Quadratic Equations - Part 3

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Ex 4.3 ,1 Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2x2 ā€“ 7x + 3 = 0 2x2 ā€“ 7x +3 = 0 Dividing by 2 (2š‘„2 āˆ’ 7š‘„ + 3 = 0)/2=0/2 2š‘„2/2 ā€“ 7š‘„/2 + 3/2=0 x2 ā€“ 7š‘„/2+3/2=0 We know that (a ā€“ b)2 = a2 ā€“ 2ab + b2 Here, a = x & ā€“ 2ab = ā€“ 7š‘„/2 ā€“ 2xb = āˆ’7š‘„/2 b = āˆ’7š‘„/(2(āˆ’2š‘„)) b = 7/4 Now, in our equation x2 āˆ’7š‘„/2+3/2=0 Adding and subtracting (7/4)^2 x2 āˆ’7š‘„/2+3/2+(7/4)^2āˆ’(7/4)^2=0 x2 +(7/4)^2āˆ’7š‘„/2+3/2āˆ’(7/4)^2=0 (š‘„āˆ’ 7/4)^2+3/2 āˆ’(7/4)^2=0 (š‘„āˆ’ 7/4)^2+3/2āˆ’49/16=0 (š‘„āˆ’ 7/4)^2+(3(8) āˆ’ 49)/16=0 (š‘„āˆ’ 7/4)^2+(24 āˆ’ 49)/16=0 (š‘„āˆ’ 7/4)^2āˆ’25/16=0 (š‘„āˆ’7/4)^2=25/16 (š‘„āˆ’7/4)^2=(5/4)^2 Cancelling square both sides š‘„āˆ’7/4 = Ā± 5/4

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