Roots of x^3 + ax^2 + bx + c = 0

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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
 
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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.
 

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