Question

How do you determine p(c) given `p(x)=x^2-4x+1` and `c=2-sqrt3`?

Answer 1

`p(c)=0`

Explanation:

`"to evaluate p(c) substitute " x=2-sqrt3" into p(x)"`

`rArrp(color(red)(2-sqrt3))=(color(red)(2-sqrt3))^2-4(color(red)(2-sqrt3))+1`

`"distributing gives"`

`color(white)(rArrp(2-sqrt3))=4-4sqrt3+3-8+4sqrt3+1`

`rArrp(2-sqrt3)=0`