Question

Find the roots of 2x2+x-4 by completing the square method

Answer 1

finding roots of quadratic equation by completing square method

2x^2 + x - 4 = 0

2x^2 + x = 4

divide by 2 on both the sides

x^2 + ( x/2 ) = 2

Adding both the sides =

= (1/2 x coefficient of x) ^2

= ( 1/2 x 1/2 )^2

= ( 1/4 )^2

= 1/ 16

x^2 + x(1/2) + 1/16 = 2 + 1/16

(x + 1/4)^2 =( 32 + 1)/16 = 33 /16

x + 1/4 = + [√33 / 4]

x =( +√33 / 4) - 1/4

=( + √33 - 1 ) / 4

therefor the values of x are

x = (√33 - 1) / 4

OR

x =( - √33 - 1 ) / 4