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 January 5th, 2019, 08:46 AM #1 Newbie   Joined: Jan 2019 From: Israel Posts: 2 Thanks: 0 Prove general solution for deppresed cubic equation y^3+py+q=0 given a discriminant I've been given the following problem and I can't seem to figure out the solution, would appreciate any help and direction to solution ! Let's look at the equation : y3 + py + q = 0 (*) We shall define Delta (or d in short) d = 4p3 + 27q2 Prove that : a) If d > 0 , then (*) has a single solution . b) If d = 0 , and at least one of the coefficients (p , q) =/= 0, then (*) has 2 solutions . c) If d < 0 , then (*) has 3 solutions . Thank you very much in advance ! January 5th, 2019, 01:10 PM #2 Global Moderator   Joined: May 2007 Posts: 6,770 Thanks: 700 You could write the equation as $(y-a)(y-b)(y-c)=0$ Compute p and q, noting that the coefficient of $y^2$ is 0 and then set up d. Then look at what happens to a, b, and c. Thanks from topsquark January 5th, 2019, 01:16 PM #3 Newbie   Joined: Jan 2019 From: Israel Posts: 2 Thanks: 0 Thank you very much ! Tags cubic, deppresed, discriminant, equation, general, prove, solution 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 The_Ys_Guy Differential Equations 1 February 7th, 2017 07:05 PM ineedhelpformaths Calculus 3 July 29th, 2015 05:42 AM neelmodi Differential Equations 1 February 27th, 2015 06:34 AM WWRtelescoping Differential Equations 3 October 5th, 2014 07:18 PM dunn Differential Equations 2 February 19th, 2012 03:38 AM

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