Decompossing a polynomial (keep getting the wrong result )

[Susanne217]

decompossing a polynomial (keep getting the wrong result :()

Homework Statement

Given the polynomial f(x) = -x^2 - x + 1, decompose the polynomial into linear terms

The Attempt at a Solution

I get $$(x-(-(\frac{-\sqrt{5}+1}{2}))((x-(-\frac{-\sqrt{5}-1}{2}))$$

I seem to be missing a integer factor but can't get it to fit properly. Maybe one of you guys can point out my error ? Or where I doing this wrong :)

 

[gabbagabbahey]

Well, the roots of your polynomial are $$\frac{-1\pm\sqrt{5}}{2}$$, so shouldn't you have

$$f(x)=-\left[x-\left(\frac{-1+\sqrt{5}}{2}\right)\right]\left[x-\left(\frac{-1-\sqrt{5}}{2}\right)\right]$$

?

 

[Susanne217]

Well, the roots of your polynomial are $$\frac{-1\pm\sqrt{5}}{2}$$, so shouldn't you have

$$f(x)=-\left[x-\left(\frac{-1+\sqrt{5}}{2}\right)\right]\left[x-\left(\frac{-1-\sqrt{5}}{2}\right)\right]$$

?

forgot the minus 1 I can see. Must be tired. Thanks :)