2

I have an equation:

$$x^4+ax^3−b^2$$

for which the discriminant is

$$−b^4(256b^2+27a^4)$$

If $$b≠0$$ what are the 2 real solutions to the equation? For these two solutions, what is a=?

John
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  • This is at least the 3rd time I see this question getting recreated today. Are you a bot ? – T_O Mar 25 '14 at 17:22
  • Far from it, just can't solve something and not getting much of a response to this problem. – John Mar 25 '14 at 17:24
  • Forcing the question is not a good idea – T_O Mar 25 '14 at 17:25
  • Recreating the question will not help you in finding an answer! – 7raiden7 Mar 25 '14 at 17:25
  • @7raiden7, I understand that. I deleted the previous ones, because I had some comments made... but no attempt to help – John Mar 25 '14 at 17:27
  • @both 7raiden7 and T_O; I can re-assure you both my intention was not force the question or for that matter cause any issues for others, I apologise if it's come across as that. If anyone could please help, I'd highly appreciate it. – John Mar 25 '14 at 17:30
  • I upvoted the question to give it more visibility. You should not delete an answer even if there are no interesting answers or it is answered, because some new elements may arrive at any given time in the future, and people need all previous elements to avoid repeating the same thing and to prevent duplicates – T_O Mar 25 '14 at 17:40
  • Highly appreciated. Thank you – John Mar 25 '14 at 17:41
  • This is a quartic equation. Since $\Delta<0$ the equation has two real roots and two complex conjugate roots. In the link there are the formulas for the roots explicitly, so plug in the determinant and after some arduous computations (it is not the easiest think computationally) you will have the result. Or otherwise you should come up with a simplification, which I do not see. – Jimmy R. Mar 25 '14 at 17:48
  • @ Stefanos: Euxaristo poli – John Mar 25 '14 at 17:53

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