Completing the square and Word Problems
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Completing the square and Word Problems
Last updated at April 16, 2024 by Teachoo
Ex 4.3 ,1 Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (iii) 4x2 + 4√3 𝑥+3=0 4x2 + 4 √3 𝑥+3=0 Dividing whole equation 4 (4𝑥^2+ 4 √3 𝑥+ 3)/4=0/4 (4𝑥^2)/4 + (4 √3)/4 x + 3/4=0 x2 + √3 𝑥+ 3/4 = 0 We know that (a + b)2 = a2 + 2ab + b2 Here, a = x & 2ab = √3 𝑥 2xb = √3 𝑥 2b = √3 b = √3/2 Now, in our equation x2 + √3 𝑥+3/4=0 Adding and subtracting (√3/2)^2 x2 + √3 𝑥+3/4+(√3/2)^2−(√3/2)^2=0 x2 + √3 𝑥+(√3/2)^2+3/4−(√3/2)^2=0 (𝑥+√3/2 )^2+3/4−(√3/2)^2=0 (𝑥+√3/2 )^2+3/4−3/4=0 (𝑥+√3/2 )^2=0 (𝑥+√3/2 )^2=02 Cancelling square both sides (𝑥+√3/2 )^2= ± 0 So, the root of the equation are x = (−√3)/2 & x = (−√3)/2