If `p(x) =x^(2)-4x+3,` then evaluate `p(2) -p(-1)+p((1)/(2))`.

Options

A. `(31)/(4)`
B. `(-31)/(2)`
C. `(-31)/(4)`
D. `(31)/(2)`

Answer

C

Explanation

Given , `" " p(x)=x^(2)-4x+3`
Now`" " p(2)=(2)^(2)-4xx2+3=4+-8+3=-1`
`p(-1)=(-1)^(2)-4(-1) +3=1+4+3=8`
and ` " " p((1)/(2))=((1)/(2))^(2)-4xx(1)/(2)+3` V
`=(1)/(4)-2+3=(1-8+12)/(4)=(5)/(4)`
`therefore p(2)-p(-1)+p((1)/(2))=-1-8+(5)/(4) `
`=-9+(5)/(4)=(-36+5)/(4)=(-31)/(4)`