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December 15th, 2016, 12:24 PM  #1 
Newbie Joined: Dec 2016 From: A place called UNIVERSE Posts: 8 Thanks: 0  alpha and beta roots!
α (alpha) and β (beta) are two of the roots of x^3 + ax^2 + bx + c = 0. Prove that αβ is a root of x^3  bx^2 + acx  c^2 = 0. Thanks in advance ! 
December 15th, 2016, 05:05 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
I suspect that the Fundamental Theorem of Algebra will help you out. $(x  \alpha )( x  \beta ) ( x  \gamma ) = x^3  ( \alpha + \beta + \gamma ) x^2 + ( \alpha \beta + \alpha \gamma + \beta \gamma)x  \alpha \beta \gamma = x^3 + ax^2 + bx + c \implies$ $\alpha \beta \gamma =\ c\ and\ \alpha \beta + \alpha \gamma + \beta \gamma = b\ and\ \alpha + \beta + \gamma = \ a.$ 

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