Configuring a Cubic

Algebra Level 3

Let f(x)=x3+ax2+bx+cf(x)=x^{3}+ax^{2}+bx+c be a cubic which vanishes at 11 and 22. If it is given that f(0)=4f(0)=4, find the value of a+b+c.a+b+c.

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