Complex Numbers roots of cubics

[mortal jay]

$ax^{2} + bx +c = 0$

[balmy kelp]

H α s ի

[mortal jay]

where

$\alpha = x$ and $\beta = x$

[balmy kelp]

H α s ի

[mortal jay]

and so the rules are

$\alpha + \beta = \frac{-b}{a}$

[balmy kelp]

H α s ի

[mortal jay]

$\alpha \beta = \frac{c}{a}$

[balmy kelp]

H α s ի

[mortal jay]

$\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta}$

[balmy kelp]

H α s ի

[mortal jay]

and

$\alpha^{2} + \beta^{2} = (\alpha + \beta)^{2} - 2(\alpha \beta)$

[balmy kelp]

H α s ի

[mortal jay]

what are the equivalent rules for cubics?

e.g.

$\alpha + \beta + \gamma = ?$

[balmy kelp]

H α s ի

[mortal jay]

and

$\alpha\beta\gamma = ?$

[balmy kelp]

H α s ի

[mortal jay]

and so on

[static terrace]

ax³ + bx² + cx + d = 0

$\alpha + \beta + \gamma = -b/a$

[balmy kelp]

swindle

[static terrace]

$\alpha\beta\gamma = -d/a$

[balmy kelp]

swindle

[mortal jay]

tysm