Cubic Function

$f(x)=ax^3+bx^2+cx+d,\backslash ,$

Bipartite cubics

$y^2\; =\; x(x-a)(x-b)\backslash ,$

$f(x)\; =\; \backslash sqrt\{x(x-a)(x-b)\}\backslash ,$

$(0,a)\; \backslash cup\; (b,+\backslash infty).\backslash ,$

Root-finding Formula

$f(x)\; =\; ax^3\; +\; bx^2\; +\; cx\; +\; d\; =\; (x\; -\; x\_1)(x\; -\; x\_2)(x\; -\; x\_3)\backslash ,$

$q\; =\; \backslash frac$ and

$r\; =\; \backslash frac$

$s\; =\; \backslash sqrt3\}\}$ and

$t=\backslash sqrt3\}\}$

$x\_1\; =\; s+t-\backslash frac$

$x\_2=-\backslash frac(s+t)-\backslash frac+\backslash frac\}\}(s-t)i$

$x\_3=-\backslash frac(s+t)-\backslash frac-\backslash frac\}\}(s-t)i$

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