Quartic Equation and Cubic Equation Puzzle

Quartic Equation
http://mathworld.wolfram.com/QuarticEquation.html

Cubic Formula
http://mathworld.wolfram.com/CubicFormula.html

To prove that we can solve a particular cubic if we can solve a particular quartic.

For example,

If $a, \; b, \; c, \; d$ are roots of a quartic equation, then $(a \, b + c \, d)$ is a root of a cubic equation

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