Polynom/x^4-x^3/Doppelte Tangente/Aufgabe

Betrachte die Funktion

{}F(x)=x^{4}-x^{3}\,.

Finde ${}a,b,c,d\in \mathbb {R}$ derart, dass

{}x^{4}-x^{3}=(x-a)^{2}(x-b)^{2}+cx+d\,

gilt.

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