They call it Newton's Sum?

Algebra Level 4

Consider \(a,b,c\) as complex and irrational numbers which satisfy:

\(a+b+c=1\)

\(a^{2}+b^{2}+c^{2}=4\)

\(a^{3}+b^{3}+c^{3}=9\)

If \(a,b,c\) are roots of monic polynomial \(x^{3}+px^{2}+qx+r\).

Find \(p+q+r\)

Note:

Answer correctly up to three digits.

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