If the expression ` x^(2) + x + 1 ` is written in the form `( x + (1)/( 2))^(2) + q^(2)` then the possible values of q are

Options

A. `+(1)/(3)`
B. `+-(sqrt(3))/(2)`
C. `+-(2)/(sqrt(3))`
D. `+-(1)/(2)`

Answer

B

Explanation

`x^(2)+1+1= (x+(1)/(2))^(2)+q^(2)`
`rArr x^(2)+x+1= x^(2)+(1)/(2)xx 2xx x+((1)/(2))^(2)+q^(2)`
`rArr x^(2)+x+1=x^(2)+x+(1)/(4)=q^(2)`
`rArr q^(2)=1-(1)/(4)=(3)/(4)`
`:. q+-(sqrt(3))/(2)`