solving a simple polynomial equation?

Question

I am looking for a solution to an equation of the form $a x^4 + b x + c = 0$.

(I need the positive solutions only, but I can filter the negative ones out, if I get the four solutions for the above.)

Is there a general way to derive a solution for this equation?

http://en.wikipedia.org/wiki/Quartic_function – Claude Leibovici Jun 19 '14 at 18:21 — Claude Leibovici, Jun 19 '14 at 18:21

score 1 · Accepted Answer · answered Jun 19 '14 at 18:22

1

Over the field of real numbers this equation need not have any solutions, e.g. for $(a,b,c)=(1,0,1)$ we have $x^4+1=0$, which clearly has no real solutions. Over the complex numbers all four solutions can be written down by Ferrari-Cardano's formula.

answered Jun 19 '14 at 18:22

Dietrich Burde

130,978

solving a simple polynomial equation?

1 Answers1