Verified answer

the roots are 2, 1+sqrt(3), 1-sqrt(3)

so you write your equation as f(x)=(x-2)(x-(1+sqrt(3)))(x-(1-sqrt(3)))

which you can expand if you need to get

x^3-4x^2+2x+4

btw i expanded using this handy tool

http://www.quickmath.com/webMathematica3/quickmath...

If r is a root, then x - r is a factor. Just make all of those into factors.

(x - 2)(x - 1 + sqrt(3))(x - 1 - sqrt(3)) = 0

If you're supposed to express it as a polynomial, then multiply that out. You do need to do some work for your own homework.

(x - 1)^2 - 3 = 0

(x-2)= 0

[x-2][x^2 - 2x -2] = 0

x^3 - 2x^2 - 2x - 2x^2 + 4x + 4 = 0

x^3 - 4x^2 + 2x + 4 = 0

http://www.flickr.com/photos/dwread/7921803292/