1. Sep 14, 2008

### Euler_Euclid

If $$\alpha,\beta\ and\ \gamma$$ are the roots of the eqn.

(x-a)(x-b)(x-c)+1=0

then show that $$(\alpha-x)(\beta-x)(\gamma-x)+1=0$$

2. Sep 14, 2008

### gunch

Do you mean we should show that $$(\alpha-x)(\beta-x)(\gamma-x)+1=0$$ for all x? What about $$x=\alpha$$, isn't that a counterexample? Maybe I'm missing something vital, but to me it seems incorrect.