Newton's Sums

Algebra Level 2

\[\large P(x)=x^{3}+33x^{2}+327x+935 \]

Let \( P(x) \) be a polynomial as described above with \( a, b, c \) the roots of \( P(x) \).

Find \( a^{2}+b^{2}+c^{2} \) without solving \( P(x)=0 \).

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