solve the depressed cubic (x^3) - 15x = 4, finding all complex roots explicitly?

Answer 1

You could look at the equation and see that x=4 is root.

So the equation can be expressed as:
(x-4)*(x^2 + ax + b) = x^3 + (a-4)x^2 + (b-4a)x - 4b

Clearly b = 1, and a = 4
So (x-4)*(x^2 + 4x + 1) = 0

The roots are x = 4
and x = [-4 +/- sqrt(12)]/2
= -0.268, -3.732

Answer 2

x=-0.267949192431
x=-3.73205080757
x=4
Finding the root x=4 let reduce you (by synthetic division) the solution to a 2nd degree equation
No complex roots.

Answer 3

roots:
-.2679
-3.7321
4
...I have a calculator rogram that does it for me