I'm looking to solve the following cubic equation for x:
$\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this equation using mathematica's Solve[] function, I get one real root and 2 complex roots. However, I have tried plotting the equation for these values, and can clearly see there should be 3 real roots. How can I obtain them. I am sure the roots are real, but mathematica gives me back complex roots.
Thanks.
Solve[2 x^3 - 5 x == 2, x] // N // Chop
... If you want it in symbolic/exact form, doSimplify[x /. Solve[2 x^3 - 5 x == 2, x] // ComplexExpand]
(I'm sure this has been asked before and probably answered by Artes) $\endgroup$x/.Solve[2 x^3 - 5 x == 2, x]
gives three REAL roots, which are expressed in terms of radicals and (of necessity) use the imaginary unit sqrt(-1). That is not the same thing as having two complex roots. $\endgroup$