
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 $(ya)(yb)(yc)=0$ 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.

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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find the general solution of the differential equation  The_Ys_Guy  Differential Equations  1  February 7th, 2017 07:05 PM 
Challenging question : Cubic discriminant origin.  ineedhelpformaths  Calculus  3  July 29th, 2015 05:42 AM 
Find the general solution to this equation  neelmodi  Differential Equations  1  February 27th, 2015 06:34 AM 
General Solution for Wave Equation  WWRtelescoping  Differential Equations  3  October 5th, 2014 07:18 PM 
Finding the general solution of this differential equation  dunn  Differential Equations  2  February 19th, 2012 03:38 AM 