Question

2x^2 -3x -1 =0 by the completing square method​

Answer 1

Answer :-

Roots of the equation are 2 and - 1 / 2.

Explanation :-

2x² - 3x - 1 = 0

⇒ 2x² - 3x = 1

Divide throughout by 2

⇒ ( 2x² / 2 ) - ( 3x / 2 ) = 1

⇒ x² - ( 3x / 2 ) = 1

⇒ x² - 2( x )( 3 / 4 ) = 1

Addind ( 3 / 4 )² on both sides

⇒ x² - 2( x )( 3 / 4 ) + ( 3 / 4 )² = 1 + ( 3 / 4 )²

⇒ ( x - 3 / 4 )² = 1 + ( 3² / 4² )

[ ∵ a² - 2ab + b² = ( a - b )² ]

⇒ ( x - 3 / 4 )² = 1 + ( 9 / 16 )

⇒ ( x - 3 / 4 )² = ( 16 + 9 ) / 16

⇒ ( x - 3 / 4 )² = 25 / 16

Taking square root on both sides

⇒ √( x - 3 / 4 )² = ± √( 25 / 16 )

⇒ x - ( 3 / 4 ) = ± √25 / √16

⇒ x - ( 3 / 4 ) = ± 5 / 4

⇒ x - ( 3 / 4 ) = 5 / 4 or x - ( 3 / 4 ) = - 5 / 4

⇒ x = ( 5 / 4 ) + ( 3 / 4) or x = - 5 / 4 + ( 3 / 4)

⇒ x = ( 5 + 3 ) / 4 or x = ( - 5 + 3 ) / 4

⇒ x = 8 / 4 or x = - 2 / 4

⇒ x = 2 or x = - 1 / 2

∴ Roots of the equation are 2 and - 1 / 2.