They call it Newton's Sum?

Algebra Level 4

Consider a,b,ca,b,c as complex and irrational numbers which satisfy:

a+b+c=1a+b+c=1

a2+b2+c2=4a^{2}+b^{2}+c^{2}=4

a3+b3+c3=9a^{3}+b^{3}+c^{3}=9

If a,b,ca,b,c are roots of monic polynomial x3+px2+qx+rx^{3}+px^{2}+qx+r.

Find p+q+rp+q+r

Note:

Answer correctly up to three digits.

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