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: (iii) 4x2 + 4โ3 ๐ฅ+3=0 4x2 + 4 โ3 ๐ฅ+3=0 Dividing whole equation 4 (4๐ฅ^2+ 4 โ3 ๐ฅ+ 3)/4=0/4 (4๐ฅ^2)/4 + (4 โ3)/4 x + 3/4=0 x2 + โ3 ๐ฅ+ 3/4 = 0 We know that (a + b)2 = a2 + 2ab + b2 Here, a = x & 2ab = โ3 ๐ฅ 2xb = โ3 ๐ฅ 2b = โ3 b = โ3/2 Now, in our equation x2 + โ3 ๐ฅ+3/4=0 Adding and subtracting (โ3/2)^2 x2 + โ3 ๐ฅ+3/4+(โ3/2)^2โ(โ3/2)^2=0 x2 + โ3 ๐ฅ+(โ3/2)^2+3/4โ(โ3/2)^2=0 (๐ฅ+โ3/2 )^2+3/4โ(โ3/2)^2=0 (๐ฅ+โ3/2 )^2+3/4โ3/4=0 (๐ฅ+โ3/2 )^2=0 (๐ฅ+โ3/2 )^2=02 Cancelling square both sides (๐ฅ+โ3/2 )^2= ยฑ 0 So, the root of the equation are x = (โโ3)/2 & x = (โโ3)/2

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.