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 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
 July 23rd, 2015, 01:56 PM #2 Senior Member     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
 July 23rd, 2015, 02:25 PM #3 Global Moderator     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

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