# Newton's Sums

Algebra Level 3

If the roots of $p(x) = x^3 + 3x^2 + 4x - 8$ are $\color{#D61F06}{a}$, $\color{#3D99F6}{b}$ and $\color{#69047E}{c}$, what is the value of

$\color{#D61F06}{a}^2 \big(1 + \color{#D61F06}{a}^2\big) + \color{#3D99F6}{b}^2 \big(1 + \color{#3D99F6}{b}^2\big) + \color{#69047E}{c}^2 \big(1 + \color{#69047E}{c}^2\big)?$

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