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.