Algebra Pre-Algebra and Basic Algebra Math Forum

 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. $(x - \alpha )( x - \beta ) ( x - \gamma ) = x^3 - ( \alpha + \beta + \gamma ) x^2 + ( \alpha \beta + \alpha \gamma + \beta \gamma)x - \alpha \beta \gamma = x^3 + ax^2 + bx + c \implies$ $\alpha \beta \gamma =-\ c\ and\ \alpha \beta + \alpha \gamma + \beta \gamma = b\ and\ \alpha + \beta + \gamma = -\ a.$ Thanks from HTsds Tags alpha, beta, roots Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ThomasYTK Math 3 March 9th, 2016 12:49 AM BonaviaFx Algebra 3 January 2nd, 2015 09:06 AM Dean1884 Algebra 7 August 5th, 2013 12:45 PM Dean1884 Algebra 11 August 3rd, 2013 02:13 AM filipd Algebra 8 September 19th, 2010 04:24 PM

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