Fun With Quadratic Roots.....

Algebra Level 2

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation, \(x^{2}-4x+5=0\).

What is the value of,

\[\alpha^{3}+\alpha^{4}\beta^{2}+\alpha^{2}\beta^{4}+\beta^{3}?\]

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