My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree2Thanks
  • 1 Post By Olinguito
  • 1 Post By CRGreathouse
Reply
 
LinkBack Thread Tools Display Modes
July 23rd, 2015, 10:52 AM   #1
Newbie
 
Joined: Jul 2015
From: germany

Posts: 4
Thanks: 0

Conditions for different roots of cubic equation.

I realized the discriminant for cubic can be 123.JPG

but I don't know what conditions are needed for different results of roots.

Thank you
ineedhelpformaths is offline  
 
July 23rd, 2015, 01:56 PM   #2
Senior Member
 
Olinguito's Avatar
 
Joined: Apr 2014
From: Greater London, England, UK

Posts: 320
Thanks: 156

Math Focus: Abstract algebra
That is the discriminant of the reduced cubic equation
$\displaystyle x^3+px+q\ =\ 0$
If the discriminant is positive, the equation has three real roots. If zero, the roots are also real but there will be repeated ones. If the discriminant is negative, there is one real and two complex roots.
Thanks from topsquark
Olinguito is offline  
July 23rd, 2015, 02:25 PM   #3
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
For the general cubic $ax^3+bx^2+cx+d$ the discriminant is
$$
27a^2d^2 - 18abcd + 4ac^3 + 4b^3d - b^2c^2.
$$
Thanks from topsquark
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
conditions, cubic, equation, roots



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Roots of cubic function Ciaran Algebra 9 September 28th, 2014 07:42 AM
Roots of Cubic Function eddybob123 Number Theory 7 June 25th, 2014 02:54 PM
Cubic Roots jake6390 Algebra 3 August 22nd, 2013 05:13 PM
Roots of cubic equation Tartarus Algebra 12 October 19th, 2009 06:26 AM
conditions for distinct roots regfor3 Real Analysis 4 November 6th, 2008 12:55 PM





Copyright © 2019 My Math Forum. All rights reserved.