Problem finding roots of a depressed quartic using the Ferrari Method. I attempted to follow the Ferrari method for a depressed quartic as described at wikipedia for the function $x^4+5/8x^2-5/8x-51/256$
The roots are $-1/4, 3/4, -1/4-i$, and $-1/4+i$. However, when I follow the method, I get a $1/4, -3/4, 1/4-i$, and $1/4+i$, or each root times $-1$.
I followed the process with other depressed quartics, and sometimes they were correct, and sometimes they were, again, the negative of the correct value.
For the quartic in question, I calculated the resolvent cubic of $x^3+5/8x^2-5/8x-51/256$. Which has one real root, m = 1/8. When I use this m, I get the negative of each of the roots.
I actually went through the derivation, and it seems correct. Does anyone have any insight as to why it is sometimes incorrect?
Edit: Here is the process as laid out on Wikipedia:
$$y^4+\frac{5}{8}y^2-\frac{5}{8}y-\frac{51}{256} = 0$$
Add $\frac{p^2}{4}$ to each side: $(y^2 + 5/16)^2 = 5/8y + 9/64
$
Add $2y^2m + pm+m^2$ to each side: $(y^2 + 5/16 + m)^2 = 2my^2 + 5/8y + m^2 + 5/8m + 9/64$
Set discriminant to zero and solve for m: $8m^3+5m^2+\frac{19}{8}m-\frac{25}{64}=0$
Use real root: $m=\frac{1}{8}$
Final equation is: $\left(y^2+\frac{5}{16}+\frac{1}{8}+\frac{1}{2}y+\frac{5}{8}\right)\left(y^2+\frac{5}{16}+\frac{1}{8}-\frac{1}{2}y-\frac{5}{8}\right)$
or: $\left(y^2+\frac{27}{16}+\frac{1}{2}y\right)\left(y^2-
\frac{3}{16}-\frac{1}{2}y\right)= 0$
The roots of the right side are $-\frac{1}{4}$ and $\frac{3}{4}$
I'll simplify the wikipedia final equations for comparison.

The roots of 
$$y^2-\frac y2-\frac3{16}=0$$ are indeed $\color{red}-\dfrac14$ and $\color{red}+\dfrac34$.
Seems that you need to review your quadratic solver :)
